Tacabrutideg and Sonrotoclax, With Response-Guided Obinutuzumab, for the Treatment of Chronic Lymphocytic Leukemia (CLL)/Small Lymphocytic Lymphoma (SLL)

Inclusion Criteria:

* Age \>= 18 at time of study enrollment who are capable of giving written informed consent, which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol
* Confirmed diagnosis of CLL/SLL by 2018 International Workshop on Chronic Lymphocytic Leukemia (iwCLL) criteria
* Meets criteria for treatment for iwCLL criteria
* Measurable disease, as defined by at least one of the following:

  * At least one lymph node \> 1.5 cm in longest diameter, as measurable by computed tomography (CT) or magnetic resonance imaging (MRI)
  * Clonal lymphocytes \>= 5 x 10\^9/L present on peripheral blood cytometry
  * Bone marrow involvement of at least 30% by flow cytometry with peripheral blood cytopenias
* Has not received any other CLL-directed therapy (e.g., must be TN). Patients who have received treatment for the treatment of immune thrombocytopenia or autoimmune hemolytic anemia (e.g. with rituximab or steroids) will be eligible if last treatment was \>= 6 months prior to enrollment
* Eastern Cooperative Oncology Group (ECOG) performance status of 0-2
* Absolute neutrophil count (ANC) \>= 0.75 x 10\^9/L if bone marrow involvement; otherwise, \>= 1.00 x 10\^9/L

  * Growth factor and/or transfusion support is permissible to stabilize participant prior to study treatment if needed. Patients must be free from growth factor support as evidenced by an ANC dated \>= 14 days following the most recent administration of peg-filgrastim (or other pegylated myeloid growth factors) and \>= 4 days following the most recent administration of filgrastim or other myeloid growth factors
* Hemoglobin \>= 8.0 g/dL, unless secondary to bone marrow infiltration by the underlying malignancy

  * Hemoglobin \>= 80 g/L (independent of growth factor support or transfusion, defined as no growth factor support for \>= 7 days and/or transfusion for \>= 3 days); patients may have hemoglobin \< 80 g/L with or without growth factor or transfusion as above if the reduced hemoglobin is secondary to bone marrow infiltration by the underlying malignancy
* Platelets \>= 50,000/uL

  * Growth factor and/or transfusion support is permissible to stabilize participant prior to study treatment if needed
* Creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 30 mL/min for participants with creatinine levels \> 1.5 x institutional ULN

  * Creatinine clearance (CrCl) should be calculated per institutional standard
* Women of childbearing potential (WOCBP) must be willing to use a highly effective method of birth control and refrain from egg donation for the duration of the study and following the last dose of the drug, whichever comes last. (Note: when oral hormonal contraceptives are selected, an additional barrier method is required) All WOCBP must have a negative pregnancy test =\< 7 days prior to the first dose of the study drug:

  * Duration of highly effective method of birth control following last dose of drug, whichever comes last:

    * BGB-16673: \>= 30 days
    * Sonrotoclax: \>= 7 days
    * Obinutuzumab: 18 months
  * WOCBP defined as a participant who is assigned female sex at birth and is postmenarcheal, has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus)
* Nonsterile men must also use a highly effective method of birth control along with barrier contraception and refrain from donating sperm for the duration of the study treatment period and then for the following duration:

  * Duration of highly effective method of birth control following last dose of drug, whichever comes last:

    * BGB-16673: \>= 30 days
    * Sonrotoclax: \>= 7 days
    * Obinutuzumab: 6 months
  * A man is considered fertile after puberty unless permanently sterile by bilateral orchidectomy. Men with known "low sperm counts" (consistent with "subfertility") are not to be considered sterile for purposes of this study

Exclusion Criteria:

* Diagnosis of Richter transformation
* Central nervous system disease at time of study enrollment
* Active fungal, bacterial, and/or viral infection requiring parenteral systemic therapy
* Positive serological status reflecting active hepatitis B:

  * Presence of hepatitis B virus surface antigen (HBsAg)
  * Patients with presence of hepatitis B virus core antibody (HBcAb), in the absence of HBsAg, with detectable hepatitis B virus (HBV) deoxyribonucleic acid (DNA)
  * Note:

    * Patients with presence of HBcAb but undetectable HBV DNA and who are willing to undergo HBV DNA monitoring every 4 weeks for HBV reactivation are eligible
    * Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention
* Positive serological status reflecting active hepatitis C:

  * Patients with the presence of hepatitis C virus (HCV) antibody and detectable HCV ribonucleic acid (RNA)
  * Note:

    * Participants must have completed curative anti-viral therapy for HCV at least 4 weeks prior to study enrollment and are willing to undergo HCV RNA monitoring every 4 weeks for HCV reactivation are eligible
* HIV with a detectable viral load or a CD4 count =\< 350 cells/uL at time of screening

  * Participants with HIV who do not meet the above criteria are eligible if they are on a stable antiretroviral therapy (ART) regimen (ART must not be strong CYP3A4 inducers) for at least 4 weeks prior to study entry and are compliant with ART are eligible
  * Participants with an AIDS-defining opportunistic infection in the past 12 months prior to screening are not eligible
* History of a second malignancy, except for the conditions listed below:

  * Potentially curative treatment has been completed with no evidence of disease for \>= 2 years

    * The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ, excluding carcinoma in situ of the bladder
  * Localized prostate cancer with Gleason score =\< 6
* Patients who are unable to comply with the requirements of the protocol
* History of ischemic stroke or intracranial hemorrhage within 6 months before first dose of study drug
* Patients with any major surgical procedure =\< 28 days before the first dose of study drug. Patients must have recovered adequately from the procedure and/or complications from the procedure before the first dose of study drug
* Patients with clinically significant cardiovascular disease such as the following:

  * Myocardial infarction within 3 months of the first dose of study drug
  * New York Heart Association classification III or IV congestive heart failure
  * History of clinically significant arrhythmias (e.g., sustained ventricular tachycardia, ventricular fibrillation, torsades de pointes)
  * Fridericia's formula-corrected QT interval (QTcF) \> 480 milliseconds based on Fridericia's formula. Patients with prolonged QTcF due to bundle branch block can be allowed after consultation with the cardiologists.
  * History of Mobitz II second-degree or third-degree heart block without a permanent pacemaker in place
  * Uncontrolled hypertension as indicated by a minimum of 2 consecutive blood pressure measurements showing systolic blood pressure \>= 160 mmHg and diastolic blood pressure \>= 100 mmHg at screening
* Patients who have received corticosteroids given with antineoplastic intent (symptom control will not be considered as antineoplastic intent) =\< 7 days before the first dose of study drug. Note: A short course (=\< 7 days) of systemic steroid use is allowed if needed to control CLL/SLL-related symptoms and it is tapered off within 5 days after initiation of study drug. Ongoing systemic corticosteroid treatment (defined as \>= 10 mg/day of prednisone or equivalent) is not allowed unless willing to receive anti-fungal prophylaxis during the entire treatment period
* Requires treatment with warfarin or other vitamin K antagonists
* History of known bleeding disorder such as hemophilia A, hemophilia B, von Willebrand disease, or history of spontaneous bleeding requiring blood transfusion or other medical intervention
* Patients who have a history of severe allergic reactions or hypersensitivity to the active ingredients of the study drug(s)
* Female patients who are pregnant or are breastfeeding
* Patients who are unable to swallow tablets or with disease/procedure significantly affecting gastrointestinal function such as malabsorption syndrome, resection of the stomach or small bowel, bariatric surgery procedures, symptomatic inflammatory bowel disease, partial or complete bowel obstruction, or gastrointestinal perforation or fistulae. Note: Gastroesophageal reflux disease under treatment with proton-pump inhibitors is allowed (assuming no drug interaction potential)
* Patients with known contraindications to azole antifungal agents, including hypersensitivity reactions