is it considered an inn to gain rested xp?
can i hearth to garrison and log and get it?

You can log off in garrison and get rested don't need an inn for it.

Rule of thumb: If you instantly log out and not do the wait 20 seconds, you'll get rested

that is how i already think of it just wasn't sure about the garrisons because i googled it and got some people saying some bugs exist

All my characters were logged off in the garrison and get rested.