[31/44] Enable TS strict mode in portlets-dot-experiments-portlet

Description

Part of the strict-mode rollout epic #35932. Enable TypeScript strict mode for the portlets-dot-experiments-portlet project using typescript-strict-plugin.

• Dependency layer: 6 (0 = leaf library, 10 = top-level app)
• Internal dependents: 1 project(s)
• Rollout order: 31 / 44

All internal dependencies of portlets-dot-experiments-portlet should already be in strict mode before starting (they appear earlier in the rollout order).

Acceptance Criteria

• portlets-dot-experiments-portlet's src is added to the typescript-strict-plugin strict paths config.
• All resulting type errors are resolved (no new any; use explicit types).
• // @ts-strict-ignore is used only where unavoidable, each with a follow-up TODO.
• yarn nx run portlets-dot-experiments-portlet:lint passes (and :build / :test where applicable).
• npx tsc-strict passes for portlets-dot-experiments-portlet.
• yarn nx affected -t build does not break dependents.

Priority

Medium

Additional Context

One project in the bottom-up rollout tracked by epic #35932. Depends on the bootstrap task being merged and on lower-layer projects already being strict.

Start by locating the portlets-dot-experiments-portlet project configuration and the typescript-strict-plugin strict paths configuration, then run npx tsc-strict for the project to enumerate errors. Resolve the reported errors without new any types, using ts-strict-ignore only with follow-up TODOs. Verify with the listed lint, build, test, strict-check, and affected-build commands, after confirming the bootstrap and lower-layer prerequisites are merged.