fix(studio): handle unexpected exceptions in updates thread

[shcheklein]

Continuation of #860

Fixes #858

We catch properly unexpected exceptions in Studio updates thread and continue consuming from the queue (to make it empty so join below doesn't hang).

TODO:

• Add test

---

• ❗ I have followed the Contributing to DVCLive guide.

• 📖 If this PR requires documentation updates, I have created a separate PR (or issue, at least) in dvc.org and linked it here.

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[codecov]

Codecov Report

Attention: Patch coverage is 95.45455% with 1 line in your changes missing coverage. Please review.

Project coverage is 95.34%. Comparing base (4309f21) to head (af72738).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/dvclive/live.py	87.50%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #864      +/-   ##
==========================================
- Coverage   95.35%   95.34%   -0.01%     
==========================================
  Files          55       55              
  Lines        3979     3999      +20     
  Branches      309      311       +2     
==========================================
+ Hits         3794     3813      +19     
  Misses        138      138              
- Partials       47       48       +1     

Flag	Coverage Δ
dvclive	95.34% <95.45%> (-0.01%)	⬇️

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