refactor: Migrate distributed to common

[achimnol]

Make PgAdvisoryLock a manager-local implementation detail.

[codecov]

Codecov Report

Merging #570 (486b50c) into main (a32c812) will decrease coverage by 0.12%.
The diff coverage is 76.47%.

@@            Coverage Diff             @@
##             main     #570      +/-   ##
==========================================
- Coverage   49.35%   49.23%   -0.13%     
==========================================
  Files          55       55              
  Lines        9137     9109      -28     
==========================================
- Hits         4510     4485      -25     
+ Misses       4627     4624       -3     

Impacted Files	Coverage Δ
src/ai/backend/manager/pglock.py	69.23% <69.23%> (ø)
src/ai/backend/manager/idle.py	30.63% <100.00%> (+0.24%)	⬆️
src/ai/backend/manager/scheduler/dispatcher.py	26.91% <100.00%> (+0.18%)	⬆️
src/ai/backend/manager/server.py	60.36% <0.00%> (-1.58%)	⬇️
src/ai/backend/manager/api/auth.py	48.44% <0.00%> (+0.51%)	⬆️
src/ai/backend/manager/models/utils.py	80.85% <0.00%> (+2.83%)	⬆️

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