Registration email link is broken

Where are you trying to put the confirmation link? It's only meant for the "Pending Email Body" parameter. It won't do anything in the "Welcome Email Body" or any other email for that matter. I've just verified it works fine on Joomla 3, Joomla 4, and Joomla 5. Please be sure "Email Confirmation" is also set to "Yes" otherwise the entire confirmation flow is disabled. It's possible you've something installed forcing the confirmation configuration off as well as that is possible (e.g. CBSubs can do this during payment to bypass confirmation for example). Please also be sure CBs system plugin in Extensions > Plugins is published and public.

I'm not sure what more to suggest. At this time I am unable to confirm any issues with the confirmation flow across 3 different installs and 3 different Joomla versions. So I don't see any grounds for me to investigate. If you'd like me to investigate your install you'll need an active Professional or Developer subscription for me to look into this further since I don't suspect a bug is causing your issue, but rather conflict or configuration problem somewhere.

Also I have a problem with registration link since a couple of weeks. Currently the email is sent but opening the confirmation link the message is that "confirmation code is wrong. Check your email or spam".
What can I check to solve it?

Please read through this topic as I've provided multiple suggestions on how to solve email confirmation link issues. If you're getting confirmation code invalid errors then more than likely your mail client is mangling the URL. Ensure it contains the confirmation code. It should be a URL that looks like the following.

Non-SEO
Format Example
SEO
Format Example