Vlad I dug into this a little and found some interesting stuff in the console. My guess is they must have unfortunately tied some part of the JS to reporting to firebase.google.com and it is failing siliently with content blocking on.
With compatibility mode disabled and the other settings at their default, this shows up in the console:
[Info] Content blocker prevented frame displaying https://track.toggl.com/timer from loading a resource from https://firebaselogging-pa.googleapis.com/v1/firelog/legacy/log?key=AIzaSyCx80ru6-RXeTi3GvqkFsMVyMf-vpgIoVw (670.6df20bad3faf7955.js, line 2)
[Info] [2022-10-21T15:24:10.583Z] Performance: – "Tries left: 2." (670.6df20bad3faf7955.js, line 2)
[Info] Content blocker prevented frame displaying https://track.toggl.com/timer from loading a resource from https://o43910.ingest.sentry.io/api/4503936890568704/envelope/?sentry_key=f65ec02900844101800a77122d491b4e&sentry_version=7&sentry_client=sentry.javascript.react%2F7.15.0 (670.6df20bad3faf7955.js, line 2)
[Info] Content blocker prevented frame displaying https://track.toggl.com/timer from loading a resource from https://firebaselogging-pa.googleapis.com/v1/firelog/legacy/log?key=AIzaSyCx80ru6-RXeTi3GvqkFsMVyMf-vpgIoVw (670.6df20bad3faf7955.js, line 2)
[Info] [2022-10-21T15:24:20.587Z] Performance: – "Tries left: 1." (670.6df20bad3faf7955.js, line 2)
[Info] Content blocker prevented frame displaying https://track.toggl.com/timer from loading a resource from https://firebaselogging-pa.googleapis.com/v1/firelog/legacy/log?key=AIzaSyCx80ru6-RXeTi3GvqkFsMVyMf-vpgIoVw (670.6df20bad3faf7955.js, line 2)
[Info] [2022-10-21T15:24:30.589Z] Performance: – "Tries left: 0." (670.6df20bad3faf7955.js, line 2)
However, if I leave compatibility mode disabled and also manually disable content blocker and/or intelligent tracking prevention, the problem is still present and those same log messages are there — so, something seems different between manually changing the settings and using compatibiliy mode.
As an aside, unexpectedly, the content blocker doesn't block a request to firebase.googleapis.com while it does block firebaselogging-pa.googleapis.com.
https://firebase.googleapis.com/v1alpha/projects/-/apps/1:744884606549:web:1e7b92771f31bd9c/webConfig