How to tell if lightly clogged shower drain has a venting problem?
One option is to get a camera or find a plumber who has a camera that can feed it into the drain to actually see what the issue is.

Another if you're concerned the problem is the vent is to go on the roof and snake the vent.

The issue could be anything from an object that went down the drain lodged in the pipe that the snake goes by without clearing to roots which will grow back over time.