To my understanding, you claim the first collected interest by an HBD transaction like a transfer. Then you can't collect the rewards for the next 30 days no matter how many transactions you do.
That 30 days time is a timer from the claiming operation itself. Like a cooldown.
so... always accruing...?
Yes, I think it's daily. I will update this comment once got confirmation from others.
EDIT: It seems the interest is calculated per second.