Integrate the remaining modernization work on dev and cut a release candidate

[coder13]

Goal

Make dev the single tested integration point for the modernized stack before promoting it to master.

Context

• PR Add PostgreSQL dual writes and room metrics #171 (PostgreSQL dual writes and metrics) is merged into dev.
• PR Modernize legacy dependencies #172 (React/MUI/tooling modernization and UI fixes) is green but still targets master.
• PR Persist solves by hiding expired rooms #140 (preserve room solves by hiding expired rooms) is based on an old master and currently conflicts.
• dev is six commits ahead of master.

Acceptance criteria

• Rebase or retarget Modernize legacy dependencies #172 onto the latest dev, resolve overlaps with the PostgreSQL/shared-module work, and keep all checks green.
• Triage Persist solves by hiding expired rooms #140 against Persist room solve history and past sessions #160: either defer it into the persistence sequence or rebase/split it if its scope is intentionally included; it must not silently block the base modernization release.
• Complete Test dev merge commits and document the dev-to-master release workflow #177 so the integrated dev merge commit is checked and the promotion process is documented.
• Run lint, unit tests, build, Cypress, and Prisma schema/migration checks on the integrated release candidate.
• Open a reviewed dev → master promotion PR with release notes and known rollout risks.
• Close or supersede obsolete open branches/PRs only after their unique changes are accounted for.

Non-goal

Do not bundle new product features into the release candidate beyond work explicitly accepted during release triage.