[api-extractor] Reduce package name lookup overhead

[gwosti]

Summary

• Reduce external package-name lookup filesystem work by reusing TypeScript's cached module and type-reference resolutions. This complements [api-extractor] Optimize the analysis type-check pass #5891 without depending on it.
• Preserve existing package-name behavior with a package.json fallback and regression coverage for deep imports, @types, and symlinks.

Benchmarks

node ../api-extractor/bin/api-extractor run --local; for i in 1 2 3 4 5; do strace -qq -f -e trace=statx -o /tmp/ae-$i.strace node ../api-extractor/bin/api-extractor run --local; awk '/AT_SYMLINK_NOFOLLOW/{n++} END{print n+0}' /tmp/ae-$i.strace; done from apps/rush-mcp-server on Node 22.18.0, median of 5 runs after 1 warmup.

Metric	Before	After	Change
AT_SYMLINK_NOFOLLOW calls	1,183	1,059	-124 (-10.48%)

Validation

• (cd apps/api-extractor && ./node_modules/.bin/heft test --clean --test-path-pattern Extractor-package-name)
• node common/scripts/install-run-rush.js test --to @microsoft/api-extractor --production
• node common/scripts/install-run-rush.js test -t tag:api-extractor-tests --production

[gwosti]

@microsoft-github-policy-service agree