Ruben De Semprun 

I guess there are two parts to this:

1. why can't you use Google Translate through your Trados Studio Freelance Plus?  What happens?
2. To use Google Translate in Trados Studio and not via Cloud-based resources you could use the MT Enhanced application: https://appstore.rws.com/Plugin/19

We have actually stopped supporting this now, but it should be fine for your needs.  Once you migrate to Trados Studio 2022 you will be able to work with this one, https://appstore.rws.com/Plugin/174 , as we separated Microsoft and Google from MT Enhanced and have improved them both.  But these are not available for earlier versions.

We have tried the solution offered by you, installed the Plugin and
launched it, and it turned out we need to enter the Google API Key. We
must have had free Google API keys for our Trados Studio 2021 licenses,
but unfortunately they have been lost. Please advise how we can recover
our Google API keys. Thank you!

Ruben De Semprun 

You would never have received free Google API keys, and certainly not from us.  You get these from your Google Account.  They'll be in here somewhere:

https://console.cloud.google.com/translation/dashboard

Thank you Paul!

Thank you Paul!