My sons attended different NorCal Division 2 schools in the same athletic conference, so I was pretty familiar with their programs, as well as with others in our conference and in some neighboring conferences.
I think you sort of answered your own question - overall, at most schools off- season conditioning is the player's responsibility. Partly because, as you note, coaches are not paid to be full-time, year round employees, and partly because usage of school gyms and weight facilities has to be shared with other teams, and the in-season sports get priority.
You didn't ask, but as for off season practices and games, I would say it's all over the map. Some schools have robust fall ball programs Some of those welcome a few players from nearby schools. Some have zilch. Even those that do have programs are usually missing key players to football, soccer, etc. BTW these programs usually have fees that help the coaches make a little more money.