Feature request: a way to bind pager-outputting command and to directly search

[psprint]

I have a very useful idea/config - make errors browser - point the error and press enter to open editor on it (details available at: https://stackoverflow.com/questions/68493494).

However, I also need to quickly jump to the errors by searching for a fixed regex "(error:|warning:)", hence the question:

Is there a way to directly search for a particular string from a binding?

Also, I would like to run :!make from a binding, however none of the available shell-command prefixes (i.e.: +,!,@,>,<) seem to be capturing the output to the pager. Hence, the 2nd question: Is there a way to run a shell command from a binding and make it output to the pager?