Have you tried e.g. vanilla Edge or Chrome (or possibly Chromium if you are in Linux), to see if you still gets those awful recaptchas?

I am pretty sure (vanilla) Firefox shouldn't produce similar problems either, as I used to use it at gog.com quite a lot in the past.

It would be interesting know what exactly triggers captchas (why some practically never see them on gog, and some like you see constantly), but I am unsure if even GOG knows it, if it is up to some super secret Google AI thingamaling.

Answer and speculation.

I have not tried vanilla Edge or Chrome.

The reCaptcha only seems to appear within the next 24 hours after any download from my library. If I keep signing in with the verification, it keeps reappearing. If I wait a day or two without attempting to sign-in, (time difference between this and previous post from me) the reCaptcha does NOT appear. Not there today.

So I believe there is a timer applied after any download which is triggered in my case due to my particular Browser and it's specific configuration falling into some predefined ruleset from reCaptcha. Perhaps next time the box appears, I will
try Chrome and/or each of the other used browsers in their stock form to see how results change.