I would not consider working for a company that required a 2 minute slack response time, especially for a role that required uninterrupted focus. Different story if you are in a "put out fires" role

Is it more important to actually get stuff done or to be available for every distracting slack message that comes through?

If you need people to respond within 2 minutes to every message, that is lack of organization imo unless it is an emergency.

Good remote teams are very organized, prioritize documentation, have weekly and sometimes daily kick off meetings and then for the most part get out of the way for their team to get stuff done.