chore(lint): add core/webview to no-floating-promises ratchet

[edelauna]

Background

The repo is rolling out @typescript-eslint/no-floating-promises directory by directory (see src/eslint.config.mjs). Currently covered: activate/** and core/task/**. core/webview/ has not been added yet.

Problem

Running the rule against core/webview/** today surfaces 89 violations, almost all in webviewMessageHandler.ts. Not all are bugs — many are intentional fire-and-forget calls — but the noise means real ordering bugs hide undetected. One such bug was found in PR #912: invalidateAll() was called without await immediately before reconcile(), silently swallowing errors and making the ordering guarantee non-obvious.

What needs doing

1. Triage the 89 violations in core/webview/ — for each one either:
   • Add await if ordering or error handling matters
   • Prefix with void if fire-and-forget is genuinely intentional
2. Add core/webview/**/*.ts to the files glob in src/eslint.config.mjs so future violations are caught at lint time

Reproduction

cd src
npx eslint --rule '{"@typescript-eslint/no-floating-promises": "warn"}' \
  --parser-options 'project:true,tsconfigRootDir:.' \
  'core/webview/**/*.ts'

89 warnings as of commit 38ae51e.