I have a question.
Are there any issues with storing the cache in system_attrs of Study?
I feel that storing cache as an attribute of the Study would be more semantically appropriate.

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 88.43%. Comparing base (440d03a) to head (329dcdf).
⚠️ Report is 885 commits behind head on master.

@@            Coverage Diff             @@
##           master    #6128      +/-   ##
==========================================
+ Coverage   88.39%   88.43%   +0.04%     
==========================================
  Files         207      207              
  Lines       14036    14051      +15     
==========================================
+ Hits        12407    12426      +19     
+ Misses       1629     1625       -4     

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I noticed a concern, so let me leave a note here:

In principle, this PR should speed up TPESampler in many cases, but it could also have a negative impact.
One example happens in combination with RDBStorage due to the exceed max string length error.
We probably need to consider an option to deactivate this caching feature if the RDBStorage does not allow us to cache a long string.

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