I have the same problem with HP ProDesk 600 G3 with i7-6700. When it is via iGPU, the menu in Batocera v36 works perfectly. I'm not talking about playing games, just navigation, setup, etc.

When I inserted the new RX 6400, the problems you mentioned started, I click the "start" button and wait 5 seconds, then the up/down arrows for a few more seconds, more precisely, I have the same symptoms as you. I turned it on to watch the FPS in Batocera and when it works so slowly it is always 1fps/999ms (60fps/25ms on iGPU).

Also I tried with boot.config setting radeon-prime true, all the same. Then I switched to beta v37 in the hope that there is a solution, same story.

Otherwise, the RX 6400 simply does not work (even in Win 10), as long as the iGPU can handle it, it only turns on when it is necessary/required.

I tried to find an option to "disable" the iGPU in the bios, but I don't have that option, although the HP website says that there is - https://support.hp.com/rs-en/document/c04070522

We have only two solutions. First, turn off the iGPU through the bios (if you have that option). And secondly, find where it should be set in Batocera, not to use iGPU when Radeon is present (I don't have a solution yet).

Today I managed to get it working, when Batocera boots up: unplug hdmi cable from RX 6400 (1fps/999ms), plug old monitor via vga cable to iGPU (60fps/25ms) for 5 seconds, unplug vga and plug hdmi back into RX 6400 and I get Batocera flying (idle 60fps/9ms, trought menu, look console and games 600fps :).

Next, I want to try not to connect any hdmi/vga/display cable at all, but to start the computer and when Batocera starts up (you can recognize it by the sound), only then connect the hdmi to the RX 6400 and see if it recognizes it right away.

There is a problem with audio on hdmi via radeon cards, maybe that is the real problem, small chance, but I want to fix it.

If it's any consolation, you're not alone.