Does Craft / Twig support regex groups? I see Craft does support regex in replace search. But there is no info on using regex groups, ie string | replace('/this is a (string)/', 'This is another $1').

Is this feature implemented? If so - how?
Yes.

{{ 'this is a string'|replace('/this is a (string)/', 'This is another $1') }}


will output

This is another string


When you pass something that looks like a regex into the |replace filter,  preg_replace() is called behind the scenes, so |replace can do anything preg_replace() can do.