[elierotenberg]

The JavaScript tooling ecosystem is adopting Oxc, and the maintainers'
other projects are moving their formatting and linting to it. Staying on
Biome here would keep a separate toolchain, configuration, and editor
setup to maintain. Separately, several release control tests accept
any failure: the publication checks search the whole error message,
which also contains the script text with every expected ::error::
line, and the tag checks accept any rejection or the fixture's own
catch-all error.

Replace Biome with Oxfmt for formatting and Oxlint with type-aware rules
for linting, keep the rules Biome enforced, and adapt the code and tests
to the stricter checks. Assert the exact errors the release controls
report.

repository:

• Format TypeScript, JSON, Markdown, and YAML with Oxfmt, keeping the
  previous line width and import grouping.
• Sort the top-level keys of the package manifest with the formatter.
• Lint with the correctness, suspicious, perf, and pedantic categories
  plus Oxlint equivalents of Biome's recommended rules.
• Give extension host tests a nested TypeScript project so type-aware
  rules resolve their Mocha types.
• Run both tools through the existing check, fix, and format scripts.
• Describe the new tools in the agent guide and the coding style
  skill.
• Adjust sources to the new rules without changing behavior.
• Type test mocks with their real contracts and assert the exact
  errors thrown.
• Read registered callbacks from mocks instead of no-op placeholders.
• Run the packed CLI's signal check as its own POSIX-only test.

devcontainer:

• Use the Oxc extension for formatting and fixes on save.

extension:

• Mark the queue poll interval callback as intentionally unawaited.

release:

• Anchor publication step errors to the annotation line they print.
• Assert the exit status of steps that fail without output.
• Assert the exact tag verification failures, including a synthetic
  history check failure.
• Validate GitHub response chunks before counting them.