[Spike] Improve connection pooling settings tracking and configuration management

[exalate-issue-sync]

Improve connection pooling settings tracking and configuration management. We got into a pickle with the deploy to test - notes are here 🔒 https://fecgov.slack.com/archives/C02TE9RJEBE/p1771522159637429 🔒

Ideate a solution to avoid misconfiguring the number of instances, workers, and threads with respect to the number of connections available on the database. This could be a programatic solution or a procedural solution (or combination of both)

Example thought process:

~15 + (api connections) + (celery connections) < db max connections? how are we tracking db max connections? Should we ingest it from the environment? Save it in the manifest?

Implementation ticket: https://fecgov.atlassian.net/browse/FECFILE-2776?focusedCommentId=50506

QA Notes

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DEV Notes

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Design

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See full ticket and images here: FECFILE-2910