fix(logs): Don't gate user behind send_default_pii

[AbhiPrasad]

ref getsentry/sentry-docs#13974

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 80.65%. Comparing base (7f8571c) to head (f6304d4).
Report is 3 commits behind head on master.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4453      +/-   ##
==========================================
- Coverage   80.68%   80.65%   -0.03%     
==========================================
  Files         142      142              
  Lines       15986    15986              
  Branches     2732     2732              
==========================================
- Hits        12898    12894       -4     
- Misses       2230     2232       +2     
- Partials      858      860       +2     

Files with missing lines	Coverage Δ
sentry_sdk/client.py	79.57% <100.00%> (ø)

... and 3 files with indirect coverage changes

[szokeasaurusrex]

Let's wait until my comment here is resolved before reviewing