Raise explicit pickle errors when `distributed.pickle.{loads|dumps}` fails

[hendrikmakait]

Supersedes #8882

• [ ] Tests added / passed
• [ ] Passes pre-commit run --all-files

[github-actions[bot]]

Unit Test Results

_See test report for an extended history of previous test failures. This is useful for diagnosing flaky tests._

    25 files  ± 0      25 suites  ±0   10h 19m 17s :stopwatch: - 5m 24s  4 131 tests + 1   4 015 :white_check_mark:  - 1    110 :zzz: ±0   6 :x: + 2  47 720 runs  +12  45 606 :white_check_mark:  - 3  2 095 :zzz: ±0  19 :x: +15 

For more details on these failures, see this check.

Results for commit 53f0039e. ± Comparison against base commit ecee9e8c.

:recycle: This comment has been updated with latest results.