The problem isn’t MongoDB on ARM (pre-built ARM64 packages of community edition are published by the company for macOS, debian, ubuntu, etc.), the problem is the Broadcom chip used on Pi 4’s being too old.
I have built and published MongoDB 6.0+ for Pi’s that do (Pi 5) and don’t (Pi 4) meet the microarchitecture requirements of MongoDB here. I bundle these binaries in a docker image and publish that on Github here as well. These will work for personal use, I would not recommend using them in production because they are unsupported by the company.
You should be able to use the ARM64 pre-built binaries from the company on a Pi 5 now, though you won’t see much official documentation about it, and I do not know if docker images for the Pi 5 are in the works.
File an issue on either of those repos if you have further issues using these unofficial Raspberry Pi images that I maintain. I hope this helps.