Add lightweight DB healthcheck to root API for `DEDICATED_SEALED_TX_MODE=1` #288

Job	Run time
Lint check (ruff)	5s
Build docker image	2m 24s
Migration tests (PostgreSQL)	1m 51s
Unit tests (PostgreSQL) (tests/app/)	21m 1s
Unit tests (PostgreSQL) (tests/batch/)	11m 21s
collect_coverage	2m 19s
	39m 1s

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