CI matrix: run server tests against SQLite and PostgreSQL

[peteski22]

Part of #257 — Phase 2 step (5).
RFC: #275.

Blocked by the testcontainers fixtures Phase 2 child.

Scope

Update CI to run the server test suite against both backends. Matrix
job: backend ∈ {sqlite, postgres}. Postgres job uses Docker for
testcontainers. Both jobs are required for merge.

Definition of Done

• CI workflow change merged and green on a no-op PR (e.g. README
  edit) under both matrix entries.
• Required-checks branch protection updated if applicable, or noted
  as a follow-up for a maintainer.
• Lint clean.