Check if CometLogger experiment is alive

[EtayLivne]

What does this PR do?

A tiny patch to align how the CometLogger class checks if the the underlying Comet Experiment object it holds needs to be reactivated. Solves cases where CometClient suddenly stops being able to log (e.g due to another Experiment instance being created by any other source).

Fixes #19900

PR review

---

📚 Documentation preview 📚: https://pytorch-lightning--19915.org.readthedocs.build/en/19915/

[awaelchli]

Thank you for including the test @EtayLivne, LGTM!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 53%. Comparing base (c1af4d0) to head (4c1b9ff).
Report is 88 commits behind head on master.

❗ There is a different number of reports uploaded between BASE (c1af4d0) and HEAD (4c1b9ff). Click for more details.

HEAD has 444 uploads less than BASE

Flag	BASE (c1af4d0)	HEAD (4c1b9ff)
python3.10	42	11
cpu	124	21
lightning	78	15
pytest	59	2
python3.8	33	6
lightning_fabric	9	0
gpu	4	2
examples	6	0
app	6	0
tpu	1	0
pytorch2.0	34	11
pytest-full	70	21
python3.11	18	4
pytorch_lightning	27	8
pytorch2.1	18	4
pytorch2.3	9	3
pytorch2.2	9	3
lightning_app	8	0

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #19915      +/-   ##
==========================================
- Coverage      84%      53%     -31%     
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  Files         426      418       -8     
  Lines       35293    35140     -153     
==========================================
- Hits        29628    18720   -10908     
- Misses       5665    16420   +10755