refactor: inline default implementation for more EpochManagerAdapter fns

[pugachAG]

Moves code from EpochManager to be the default implementation for EpochManagerAdapter trait.
Similar to #12851.
This should also help avoiding issues like #12913.

[codecov]

Codecov Report

Attention: Patch coverage is 67.42424% with 43 lines in your changes missing coverage. Please review.

Project coverage is 70.51%. Comparing base (e8bbcfb) to head (8e1b0e2).

Files with missing lines	Patch %	Lines
chain/epoch-manager/src/adapter.rs	70.63%	7 Missing and 30 partials ⚠️
chain/chain/src/test_utils/kv_runtime.rs	0.00%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #12923      +/-   ##
==========================================
- Coverage   70.53%   70.51%   -0.03%     
==========================================
  Files         851      851              
  Lines      174921   174921              
  Branches   174921   174921              
==========================================
- Hits       123374   123338      -36     
- Misses      46420    46452      +32     
- Partials     5127     5131       +4     

Flag	Coverage Δ
backward-compatibility	0.36% <0.00%> (ø)
db-migration	0.36% <0.00%> (ø)
genesis-check	1.42% <0.00%> (ø)
linux	70.37% <67.42%> (-0.02%)	⬇️
linux-nightly	70.15% <67.42%> (-0.02%)	⬇️
pytests	1.73% <0.00%> (ø)
sanity-checks	1.54% <0.00%> (ø)
unittests	70.34% <67.42%> (-0.03%)	⬇️
upgradability	0.36% <0.00%> (ø)

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[Longarithm]

Amazing!