No longer able to add Teams link in invite from shared calendar in browser

Seems to work fine here, but my configuration might differ from yours. Generally speaking, in order to be able to send an email as another mailbox, you need to have the necessary permissions (Send As). When it comes to calendar items/meeting invites, you must also be accessing the shared mailbox directly, as in you need to have Full access permissions on it. This is the only way you can access the corresponding UI bits in classic Outlook or OWA.

Assuming you have the necessary permissions, try opening the shared mailbox in OWA via the Open another mailbox functionality (click on your profile photo in the top right to access it). Once it opens in a new tab, you should be able to create a new event ant toggle the Teams checkbox. The join details will not appear at this point, but will be appended when the invite is sent.