I don't know what the current status is for Linux M4 support. It takes the Asahi Linux team some time to reverse engineer the new hardware changes. I think the M4 changed a lot of things.
There is an Asahi Ubuntu version as well.
https://ubuntuasahi.org/
Keep in mind these are still works in progress. There are still a lot of hardware support for even the M1s that still need work, although basic usage on the M1 & M2 Macs are fairly good for basic things. I've heard people can even play games on them. However, the M3 & M4 Macs are not quite as well off due to the significant hardware changes. You would need to follow the Asahi Linux team to discover what is and is not supported.
Also, keep in mind that the Asahi Linux installers must be run from the Asahi installer scripts while booted into macOS. Plus the Asahi Linux install process requires a large partition for Linux since there is a lot of things needed to support Linux on the M-series Macs. I forget how much storage was required and it requires macOS being able to shrink the APFS Container/partition enough, but the amount of data on your macOS volume may be too much too allow the necessary resizing.
You should also be prepare to perform a DFU Firmware Restore to completely get rid of the Linux installation....this will reset the internal SSD causing all data on the internal SSD to be destroyed. Yes, it is probably possible to remove all traces of the Linux installation without that drastic action, but I don't think your skill level is there at this time since it would involve using the command line to reclaim the storage space.
At this time, it is not possible to install Linux onto an external drive and from what I've read from the Asahi developers, it is not a priority to provide such an option.
I didn't do anything significant with my Asahi Ubuntu or Asahi Fedora installations, but I do know that there are a lot of unfinished bits there including not having all of the source code available to rebuild the Kernel while booted into Linux. The Asahi Linux developers are doing all their work outside of the main Linux installation...I think they are working from within macOS & tethering to the Linux installation to do most of their work to develop their Linux drivers. I don't recall the specifics, but they include that information in their blogs.
Oh, and make sure to follow the Asahi installation instructions exactly. The installation process requires the user to perform some manual actions and if those actions are not performed exactly as outlined, then the installation will fail and the system will remain in a mixed state. The Asahi developers make this quite clear if you take the time to read their instructions and information presented during the installation. I actually made a mistake on my second installation because I became distracted during the install process....I was able to easily recover due to my experience with Linux, but most people would end up needing to start completely over by performing a DFU Firmware Restore.
Make sure you have good backups of your data because you may need to wipe the system. You should always have frequent & regular backups anyway since there are a lot more new ways to permanently lose access to the data stored on the internal SSD of the recent Macs due to all of the hardware, software, and security changes.
Edit: I highly recommend you take @MrHoffman's advice and use a Virtual Machine to install an ARM version of Linux. This should be more than sufficient for most people.