drop @atproto/api from the dependency tree

The last references were stale comments; the package itself leaves
package.json, webpack's transpile list, and 102 packages from the lockfile.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

src/lib/strings/__tests__/errors.test.ts

@@ -94,7 +94,8 @@ describe('cleanError', () => {
   it('surfaces the authentication-required code of a lex error', () => {
     /*
      * The lex client derives `AuthenticationRequired` from a 401 with no XRPC
-     * payload, where `@atproto/api` used the spaced "Authentication Required".
+     * payload, where the pre-migration client used the spaced
+     * "Authentication Required".
      * Neither is special-cased in `cleanError`, so what matters is that the
      * class- and code-prefixed stringification does not reach the user.
      */