I bet you probably remember VirtualPC from back in the PowerPC Mac days, that emulated an x86 Intel CPU so you could run Windows XP on your Mac.
That kind of CPU architecture emulation is what you’d have to do to run the Intel-only Mac OS 10.11 and all your Intel-only software. That’s kind of what Rosetta 2 does, however Rosetta 2 will only let you run a Big Sur or Monterey-compatible Intel app in Big Sur or Monterey on M1. It won’t help you use older OSes or older apps that are incompatible with Big Sur+.
Fortunately there is an emulator available called QEMU and a Mac app called UTM that lets you emulate x86 Intel chips on an M1 Mac or even on iOS.
https://mac.getutm.app/
Theoretically with UTM you could emulate your Xeon Mac Pro system on an M1 Mac and run your existing El Capitan installation in a virtual machine similar to Parallels. I haven’t used UTM so I can’t speak to its performance. VirtualPC back in the PowerPC days was very slow, I wouldn’t have high hopes that UTM on an M1 Mac would be as good or better than the performance you’re used to. UTM also doesn’t emulate GPUs as I understand, so you’d be limited to CPU rendering and very basic GPU abilities.
My advice would be to keep your Mac Pro that you like, and when you get a new Apple Silicon Mac someday to treat it as a brand new system. You can use the built-in remote desktop features of Mac OS to connect to your existing Mac Pro and use your current apps alongside the new M1 Mac.
Another idea is you get the current 2019 Intel Mac Pro (maybe a used one from someone trading up). Or a recent Intel iMac or Mac Mini or something pretty high end. You won’t be able to boot El Capitan directly on a newer Intel Mac because El Cap lacks the drivers to support the newer Mac hardware. But you will be able to use Parallels to run your El Capitan installation as a true virtual machine on the Intel hardware, no CPU architecture emulation required. So you probably would be able to achieve equal or better performance than your existing Mac Pro.
Another possibility, build a hackintosh PC capable of running El Capitan. Or a 2012 Mac Pro which is expandable in ways the 2013 Mac Pro is not…