[Due for payment 2026-03-30] [Due for payment 2026-03-02] [Sentry] Send App logs to Sentry

[rlinoz]

Complete release 2.5 from the design doc https://docs.google.com/document/d/1nemsiB9xx16kfJnWfy6kGabsl7FQy_EWAR1lOirEOnE/edit?tab=t.0#bookmark=id.lkiawm3vhiu2

5. Pipe our logs into Sentry to let them become a part of the context.
   1. Modify Log.ts logic to send logs using Sentry’s log API
   2. At first we will filter out everything and later whitelist whatever we think is helpful. This is required to ensure no user’s PII pass through

Issue Owner

Current Issue Owner: @VictoriaExpensify

[rlinoz]

Blocked on #73301

[melvin-bot]

@adhorodyski Uh oh! This issue is overdue by 2 days. Don't forget to update your issues!

[rlinoz]

I will move this to weekly while we focus on other issues.