You get similar buffer behavior if you use :make inside Vim and Vim as your build terminal. Despite being named :make it isn't hardcoded to just make as build tool (there's a bunch of out-of-the box settings you can pick with :compiler or you can update individual settings like makeprg).

Similar behavior with :grep inside Vim which you can change your grepprg to rg if you like.

I've got a feeling the `| vim -c cd -` isn't as commonly known because the Vim-initiated versions are somewhat more commonly known. It's handy to know that vim can do it in both "directions" (initiated from the external shell / initiated to the internal shell support).