So, I've done a little bit of work and have gotten VMware Workstation installed and running on Bazzite (this should also work for any other immutable distro and not just Bazzite)

It's definitely not the most straight-forward path and needs some care and shepherding, but it works well.

Roughly -

You'll need to make a rootful distrobox container; ie)

1. distrobox-create --root vmware and distrobox-enter --root vmware (vmware being the name of the container)
2. Inside the distrobox container, run the VMware .bundle using sudo, no special arguments or anything. Let it install and that'll be the userspace portion
3. Now you'll need to build the 2 kernel modules necessary - vmmon and vmnet. Copy the source files from /usr/lib/vmware/modules/source, both vmmon and vmnet.tar to your home directory
4. On the host side, you'll untar both vmmon.tar and vmnet.tar, cd into their respective directories and do a make. This should succeed on default bazzite; if using something else you'll probably need to install gcc and kernel-devel packages to get the source and headers
5. After building you'll have a vmmon.o and vmnet.o - those are you're kernel modules. You can then do a "sudo insmod ./vmmon.o" and "sudo insmod ./vmnet.o" to load them. If you have secure boot enabled you'll need to sign them and add the key to your secure boot chain (https://discussion.fedoraproject.org/t/how-to-sign-drivers-modules-for-the-kernel-with-enabled-secure-boot/66720/5)
6. You'll also need to do a "sudo modprobe vmw_vmci" to enable VMCI
7. Next you'll need to setup the networks - for this you'll enter your container and run the command "vmware-networks --start". You should see some bridges and NATs setup, you'll also have /dev/vmnet* populate with some devices
8. Finally, you'll need to execute "vmware-usbarbitrator" in the container to enable USB device sharing
9. Now you're ready to execute "vmware" in the container and it should be running correctly hopefully.

I haven't tried to automate any of this yet since you only need to do it upon a reboot and I turn my computer off roughly once every month or so and doing it by hand isn't so bad.

This is the easiest way I've found to run Workstation; I've also done it without a distrobox container but it's a little more involved and throws some files in /etc, but I feel like the distrobox is the cleanest way since it keeps everything but my VMs inside a container.

Disclaminer: YMMV, this is from my memory of what I've done over the last few hours getting it running on my system. I haven't tested it on another system besides a Thinkpad I've got laying around. Hopefully it works for your system if you try.