2023 F-150 Horn not working?

Hello, when you say "reset the display", did you disconnect the battery or unplug the display? The Body Control Module (BCM) controls the Horn in these trucks, the switch in the steering wheel is grounded when pressed, this signals the BCM to ground the Horn relay. I think what might be happening is a diagnostic trouble code might be setting in the BCM, (which wont trigger the check engine light) and the BCM is shutting down that circuit due to a fault somewhere. I have repaired these exact issues in Ford trucks, most of the time its a wiring issue, but you will need a capable scan tool and the first thing I would do, is when the horn stops working, I would check the BCM for any stored trouble codes, and you can also look at live data from the BCM, so for example there will be a data PID (an ID) for the Horn switch. It will read On or Off depending if the horn is pressed or not. This is where if the the BCM is detecting a fault somewhere in the circuit it can most likely turn that circuit off to protect the BCM or other modules from damage.
I would also recommend to do as much with a scan tool as you can to begin with, because once the BCM connectors are unplugged, if this issue is within the wiring harness or connectors, the problem could mask itself and be very difficult to find in the future.
Ill post the wiring diagrams for the Horn circuit though, so you have them.
You'll be able to see how the circuit actually works.

The first diagram below is the Horn circuit, with the 2nd diagram being the oem Ford diagram, you can see they are both pretty much the same, but with the BCM's location in these trucks (diagrams 3,4, ignore the pedal in the 3rd diagram), I have seen a lot of water intrusion in it's location. But since you are able to reset the BCM and the Horn works for a few minutes then stops, I think you will find a code stored for the Horn relay circuit. On newer vehicles if a control module detects over current flow or the incorrect voltage on certain circuits, those circuits can be shut down until the vehicle can be looked at.
The guide below on the Check engine light just gives an example of how to read codes from modules. Being this is a very new vehicle, you will need a capable scan tool to access the networks and modules.

https://www.2carpros.com/articles/how-to-use-a-voltmeter

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Its always possible there are other related issues you just havent come across yet, the one thing you dont want to do is go unplugging and plugging back in any bulk connectors like the BCM has, if it turns out there is corrosion in the BCM's connectors, I would try some electrical terminal spray first, you can get it at any auto parts store. But have someone go into the BCM first and look at its live data and do a code scan. Just tell them you need a full system scan so you will have a list of all codes stored in any modules throughout the truck. Then we can look up each code by number and see what the code setting criteria is.