You don't want to do that. MacOS support for any modern filesystem (i.e. not crappy exFAT) that is not its blessed proprietary format, is likely to be bad or non-existent - at which point you have to install some shaky extension from a third party... The chances for anything to go Very Wrong are high. It's even worse than with Windows.

The best way to share files with a proprietary system is to go through some sort of network, i.e. NAS, smb, etc.

It should be fairly easy. Just pick a filesystem that both macOS and Linux can read/write to and format a partition accordingly (the Asahi installer won't make this third partition for you, but it should be pretty easy to figure out).

If I was going to go that route, on my MacBook which is 1TB, I would probably do something like 200GB for macOS, 200GB for Linux and then a shared partition of the rest (~600GB). I'd probably make the shared partition ExFAT, or possibly un-journaled HSF+.

I think the easiest way would be to install Asahi first, pick the size you want for it (200GB in my example), then once you have that sorted, figure out how to create another partition that you will format as ExFAT/HSF+/Whatever you want. I'm sure this is possible/easiest from the macOS side of things, although I have never partitioned a drive in macOS. The Asahi installer does it from the command line in macOS, so I'm sure Disk Utility has the ability to resize and create partitions, too.