It used to be possible to do a backup with a dead screen. I had an iPad mini 2 that was dropped really badly and nearly all the glass was gone. All I had to do was connect via a Lightning cable. The backlight sort of lit up but I couldn't see anything show up other than a purplish light. But I could see it in Find My (along with battery charge level) and I was able to create a new backup since it was already "trusted" with my Mac.
However, these days you will need a working front screen assembly in order to approve a backup. The latest versions of MacOS (even Catalina) and iTunes (for PCs) won't start a backup without the passcode being entered into the iPad first.
If it's that important to you, it might be possible to have a third party shop help you out with data recovery. We can't give you a recommendation as to who to seek. If it's just a trashed front screen assembly (and no substantial damage to the underlying hardware), it might be possible to do it with a temporarily connected working front screen assembly that you might not need to purchase. It might even be possible to get a permanent fix to it, although it wouldn't be anything that Apple would authorize and typically any such devices wouldn't be eligible for Apple's typical battery replacement service - or possibly even Apple's "other damage" replacement service.
Apple officially only offers a full replacement service where the damaged iPad has to be exchanged. They won't help with data recovery and consider it the responsibility of the customer to have backed up the data.
