refactor!: Move Base AuthClient Types to authclient.ts

[HubertJan]

Fixes #1773 🦕

[google-cla[bot]]

Thanks for your pull request! It looks like this may be your first contribution to a Google open source project. Before we can look at your pull request, you'll need to sign a Contributor License Agreement (CLA).

View this failed invocation of the CLA check for more information.

For the most up to date status, view the checks section at the bottom of the pull request.

[conventional-commit-lint-gcf[bot]]

🤖 I detect that the PR title and the commit message differ and there's only one commit. To use the PR title for the commit history, you can use Github's automerge feature with squashing, or use automerge label. Good luck human!

-- conventional-commit-lint bot https://conventionalcommits.org/

[HubertJan]

The linter was failing, I fixed that now. I hope we can merge now :)

[danielbankhead]

@HubertJan thanks! We'll merge it in the next major