Dipstick pops out

So the transmission would vent through the engine crankcase? Don't think thats even possible, or am I wrong?
you are correct not possible. When I read your post the first time I assumed Engine. Then I re read your post...
My transmission dipstick

Simple answer is rubber grommet / gasket is no longer large enough dia to keep side tension on the tube.

OR

the trans vent is clogged

OR

both

You might not have oil coming out the filler but air pressure might be and pushing the dip stick out.

upload_2018-9-22_14-53-37.png

Final thought...

is the dipstick hitting the bottom of the trans pan? check with long straight rod and compare to dip stick length.