Add flattened JSON log format support

[kitop]

Close #986

Builds on top of #822 and adds a new json_flattened log_format option that puts the fields at the top level.

Example output:

$ PGDOG_LOG_FORMAT=json_flattened RUST_LOG=info \
    cargo run -q -p pgdog -- --config /tmp/missing-pgdog.toml --users /tmp/missing-users.toml configcheck 2>&1

{"timestamp":"2026-05-19T11:24:44.191700Z","level":"WARN","message":"\"/tmp/missing-pgdog.toml\" doesn't exist, loading defaults instead","target":"pgdog_config::core"}
{"timestamp":"2026-05-19T11:24:44.192415Z","level":"WARN","message":"\"/tmp/missing-users.toml\" doesn't exist, loading defaults instead","target":"pgdog_config::core"}
{"timestamp":"2026-05-19T11:24:44.192447Z","level":"INFO","message":"[debug only] admin password: _pgdog_BApCRAcrBvNp","target":"pgdog_config::core"}
{"timestamp":"2026-05-19T11:24:44.193621Z","level":"INFO","message":"✅ config valid","target":"pgdog"}

[CLAassistant]

All committers have signed the CLA.

[levkk]

Awesome. Just run cargo run --bin pgdog-jsonschema and this should be good to go.

[codecov]

Codecov Report

❌ Patch coverage is 50.00000% with 6 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
pgdog/src/lib.rs	50.00%	3 Missing ⚠️
pgdog/src/plugin/mod.rs	0.00%	2 Missing ⚠️
pgdog-config/src/general.rs	75.00%	1 Missing ⚠️

📢 Thoughts on this report? Let us know!

[kitop]

Thanks!
Updated in eef0b07