Fingerprint sensor doesn't respond

Before you decide you've got a hardware problem, you need to exhaust all of the software fixes that are possible. Here are a couple of websites addressing issues with the fingerprint sensor on your phone; the first one is from Samsung and the second just has more ideas but you'll want to try all of these solutions first because the alternative is replacing the fingerprint sensor which is going to be difficult.

My fingerprint scanner isn't working

Fix: Samsung Galaxy S20 Series Fingerprint Scanner not working or Not Detecting

Okay, so you've gone all the way through and nothing helps. At this point the next best option would be to replace the fingerprint sensor on the assumption that it's failed. I wasn't able to locate any guide showing how to replace that sensor, but I got pretty close. The iFixit Screen Replacement guide for your phone shows how to get the screen off, and since the fingerprint sensor is mounted on the screen, once it's been removed you now have access to the sensor and can replace it. Here's where it's located on the back of the screen on your phone.

Here's the guide you'll need to get the screen off.

Samsung Galaxy S20 Ultra Screen Replacement - iFixit Repair Guide

The sensor itself seems to be available; I usually start with places like Amazon, eBay and AliExpress, but here's another site that came up on my cursory search.

Fingerprint Sensor Flex Cable Compatible for Samsung Galaxy S20 Ultra 5G

Be sure and take pictures as you remove and replace the sensor so you can create your own guide to doing that job. You can use all of the screen replacement guide as a prerequisite so most of the work has already been done for you!

Good luck and let us know what you find and how the repair goes.