Fix pickle issues in MCMC posterior + test

[manuelgloeckler]

What does this implement/fix? Explain your changes

This PR address the issue of the MCMCPosterior not being pickable after running sample.

Does this close any currently open issues?

Fixes #1278

Any other comments?

Extended the save and load tests to be performed after calling sample and log_prob once.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 78.43%. Comparing base (428fc93) to head (56c6a5e). Report is 3 commits behind head on main.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1291       +/-   ##
===========================================
- Coverage   89.30%   78.43%   -10.87%     
===========================================
  Files         119      119               
  Lines        8721     8732       +11     
===========================================
- Hits         7788     6849      -939     
- Misses        933     1883      +950     

Flag	Coverage Δ
unittests	78.43% <100.00%> (-10.87%)	:arrow_down:

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
sbi/inference/posteriors/mcmc_posterior.py	86.14% <100.00%> (-0.55%)	:arrow_down:

... and 31 files with indirect coverage changes