ci(e2e): cover additional Linux stability suites

[drew]

Summary

Expand the Linux E2E stability campaign with runnable suites that the standard branch matrix does not cover. This PR is stacked on #3584, which is stacked on #3583.

Related Issue

No issue required: this is localized CI orchestration for finding intermittent failures while validating #3583.

Changes

• Add managed Podman and Kubernetes database E2E jobs to manual stability dispatches.
• Add TypeScript interactive exec, mechanistic policy checks, and the no-driver gateway contract to a dedicated Docker stability job.
• Aggregate those jobs into a separate stability result so the existing required PR and merge-queue gate remains unchanged.
• Document the added coverage.

Testing

• mise run pre-commit passes.
• nix develop --command actionlint -shellcheck= -pyflakes= .github/workflows/branch-e2e.yml passes.
• Full GitHub stability campaign on this PR's SHA is pending.

Checklist

• Follows Conventional Commits.
• Commit is signed off (DCO).
• Architecture docs updated.

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[drew]

Closing to narrow the automated flake investigation to the four selected fixes (#3583/#3588, #3598, #3604, #3608). The findings remain available here for later follow-up.