Recently, I've seen a rise in popularity of small drones using pusher props. Some of these include the FullSpeed TinyPusher, BetaFPV Beta95X/Beta85X V2, Diatone Taycan and Tinawhoop, and originally the tinyhawk. Why are pusher prop designs for small BNF quads becoming more prominent? I haven't seen any 5-inch BNF quads with pusher props which leads me to wonder, are there advantages to having pusher props on a micro drone that wouldn't benefit larger drones as much?
I have a working theory for why this may be the case; some micro-quad designs support this theory more than others.
Due to Newton's third law, the thrust force created by the propellers also has the effect of trying to lift the propeller up off of the motor in traditional multirotor designs where the propeller is on top of the motor. Aside from ensuring that the propeller can't spin independently of the motor, this is the reason why drones have propeller nuts (or a similar mechanism) to securely hold the propeller to the motor.
Many micro-quad designs, including some of the ones you link to in the OP (e.g. the Diatone BNF TinaWhoop and the FullSpeed BNF Cinewhoop) instead feature the pusher-prop configuration you mention, with the propeller underneath the motor, and forego the inclusion of propeller nuts or bolts screwed through the propeller into the motor.
(FullSpeed BNF Cinewhoop cit.)
I don't have one of these quads to confirm my observations from looking at the images, but it appears like these designs have the propeller attached to the motor with a simpler mechanism that likely doesn't provide as much strength in the vertical direction. If my hypothesis is correct, this would mean that the propellers could theoretically fly off more easily if the motor wasn't in the way of the path the propeller wants to take during flight.
Microquads tend to be flown indoors, where the floor is relatively smooth but there are lots of other things to hit. Putting the prop under the frame provides additional protection when the quad flies into an obstruction. The direction of air flowing through a prop would tend to suck objects in from the top and blow then away from the bottom, so more protection is required on the top.
Outdoor quads often have to take off from ground that is covered with grass or other rough objects, and the additional clearance of top-mounted props decreases the chance of getting tangled.
This related question shows that there is a small performance improvement to putting the props below the frame, but these quads are not the ultra-small ones with very short flight times and marginal performance, so I think it's mainly for crash protection.