Shrink extension size for `github.dev` by only including modules which are used in `tsconfig.browser.json`

[karrtikr]

When running in browser we only need to include what src\client\browser\extension.ts imports. It uses certain file system tools, common modules like localize.ts.

With #17658 it was expanded a lot more than needed.

[karrtikr]

#17658 was corrected.