ThinkStation P340 with Intel UHD 630 cannot get display output

The points to hardware failure - most Lenovo business products comes with 3y onsite NBD repair.

I have a P330 gen2 - with Intel 630 - it just works using Manjaro.

Did you test the ports with different cables?

For the past decade I have been using Lenovo hardware for it’s stability, compatibility and supreme warranty program.

Lenovo usually comes with Windows so disabling secure boot is mandatory.

I my experience Lenovo works OOB with Manjaro - any Linux actually - so you can verify using e.g. Ubuntu or Fedora.