Home button needs to be pressed hard

based on your operation, there should have been no need to touch anything on the screen, but as a precaution, i'd remove the home button bracket (4 trilobe screws) and reconnect it. i don't think it's necessary to disconnect/reconnect the home button connector to the screen, but if you can do it safely, might be worth a try.

other things to consider, make sure the video and button connecters are properly seated. i don't recall which is which, but if if the connector is just showing bare metal, you might want to get an adhesive foam pads (check the ifixit store) on them to help the bracket hold them in.

other than that, there's not much from a simple troubleshooting standpoint since there's no mechanical action, the button reads something from the presence of a finger to read a "button press" then use the taptic engine to provide the feedback of a click.

it is possible, i've seen it, where the button portion of an Apple home button stops working (or working well) even though the Touch ID is still good. the only option here is to replace with a 3rd party home button (JC or YF - no bluetooth or soldering required) which gives you home button functionality but you lose Touch ID function, but you do get a working home button again.

Hope this helps

Good luck