If you don't have control over the EXE, I assume you're building a plugin. Then it may or may not work correctly irrelevant of whether you can get it running locally. The problem is a lot like trying to get a NET-implemented component running in the Shell before NET 4.x came out. The issue is that you might be able to bootstrap the necessary infrastructure to host the WinUI3 runtime but somebody else might have already done that (either the EXE or another plugin) so you'll end up colliding in the middle.
Irrelevant here is an article that supposedly gets it to work in an existing Win32 program by manually bootstrapping the runtime. Note that depending on the architecture of the app this might or might not work since the plugin would need to do this and if it loads late in the process it might be too late.
Perhaps a safer, albeit harder, workaround is to host the actual WinUI3 stuff in a separate process and interop with the plugin hosted in the Win32 process. This has its own set of challenges such as providing the illusion of an integrated UX when in fact they are separate, since you can't set Win32 parent-child relationships across processes. If you need to integrate directly into another UX then this wouldn't work but if your plugin merely needs to show a standalone UX then it would work.