Hi for everyone reading.
I don't exactly know what made the difference that I could get it to work this time, but it worked nontheless.
So I formatted the stick with FAT32 via the windows explorer options with 16kilobytes unit size and unchecked the quick format option. I tried using the the "SurfaceLaptop_BMR_151_16.302.2.zip" which is the "Surface Laptop 128GB M - Windows 10 Pro in S Mode Version 20H2" version. I made sure the stick was FAT32-formatted and extracted the zip-file.
I also tried using a new 32GB USB Stick, which might also could have made a difference since I used a 64GB stick before which was partioned.
Then I disabled secure boot and changed the boot order that booting from USB stick is the first priority, I reboot and it booted the OS from the stick.
I wanted to document the process for everyone stumbling across the error (including me in the case of needing to do it again) and the issue for me has been resolved.
I attached the screenshots for a better understanding.
Thanks for helping out.