The bug:

The entity is moved up ~0.05 blocks (established using carpets mod's tick freeze) and becomes stuck in the piston head. On versions 1.2.1-1.19.4, when the piston is retracted, the entity clips into the piston body and sinks through the cobweb.

Expected Result:

The piston to push the entity up a full block and the entity to sink through the cobweb.

Steps to Reproduce:

1. Place piston, facing upwards
2. Place rail on top of piston
3. Place cobweb to the top and left of the piston
4. Place minecraft on the rail and break the rail
5. Nudge the minecart into the cobweb
6. Ensure there are no block underneath the cobweb
7. Power and de-power the piston (slowly)

See the video and photos for more information on how to setup this glitch.

Responses:

Now tested for all spawn egg mobs (in response to Marty Mcfly):

• Doesn't affect Spiders / Cave spiders, as these mobs are not slowed by cobwebs.
• Doesn't affect flying mobs (Bees, Bats, Ghasts, Phantoms) or mobs summoned with

  /summon minecraft:creeper ~ ~ ~ {NoGravity:1b}

Now tested for short duration pulses (in response to Gnamf Jojo):

• Works for all pulses, down to 0-tick pulses (make sure there's no block under the cobweb)

Updates:

When a player is pushed within the cobweb, they are put into swim mode.

This glitch also affects Minecarts that are still on rails.

Code analysis

Code analysis by haykam can be found in this comment.