The December 18th release of Firebase JS SDK v4.8.1 introduced changes to firebase type definitions. See: Issue #393 Cannot find module '@firebase/app-types/private'
As of December 27th there is an open pull request that should resolve the issue. In the near term we recommend that Ionic Pro users revert to version 4.8.0. To install 4.8.0 explicitly run the following command.
npm install --save -E email@example.com
Alternatively, the version can be set to 4.8.0 explicitly in package.json. Replace the existing reference to firebase with the following.
Note that the carat (^) character is not present. Including the carat will allow for any 4.x version. See: npm semver Caret Ranges
This issue typically manifests with the error "Cannot find namespace 'firebase'", or "Cannot find module '@firebase/app-types/private'" during the transpile step.