fix(sdk): align context update types across browser React and Vue

[roncohen]

Summary

Fix a pre-existing mismatch between JSON-compatible context types and the narrower context update APIs. Split out of #770; no flag event changes are included.

• Accept typed UserContext/CompanyContext values and partial updates in the browser SDK while preserving string/number IDs.
• Derive React/Vue update-hook parameters from the browser methods so their types stay consistent.
• Align other-context updates and deprecated provider props with the existing context types.
• Add runtime/type coverage and patch changesets for browser, React, and Vue.

No JSON serialization or runtime context-merge behavior changes.

Validation

Validated independently on a branch based on main:

• Browser SDK: 194 tests passed, excluding test/sse.test.ts.
• React SDK: 65 tests passed.
• Vue SDK: 13 tests passed.
• Browser source TypeScript check and production bundles passed, with declarations restricted to source files.
• React/Vue type tests and production builds passed.
• Oxlint, formatting, and git diff --check passed.

The existing SSE tests have seven constructor-mock failures under the local Vitest 3.2.6 installation. No SSE source, tests, or repository test configuration were changed.