Even back in 2015 you didn't need to set your default browser to the IE11 desktop application to install Money. Money needed some components of the IE11 desktop application but doesn't use the IE11 browser.
The IE11 desktop application (or an earlier version) was included with all versions of Windows up to Windows 10. Money uses some components of IE11 and Money will run fine as long as you don't remove those IE11 components. You don't need to use the IE11 application as your default browser. You can use whichever browser you like.
With Windows 11, the IE11 desktop application is gone but the components of IE11 that Money needs are still installed. This is for backward compatibility with many applications, - not just Money. Going forward, it seems likely that Microsoft will continue to provide these IE11 components, but life is uncertain. Only time will tell. I expect that even if Microsoft removes components that are needed by Money (and many other applications) there will quickly be workarounds developed by computer-savvy users.
Note that with Windows 11, Microsoft is making it very difficult to have a default browser other than Edge. There is a lot of griping about this in the user community. It is not clear how this will play out.
Also note that Edge does have an "IE11 Mode" that allows Edge to access sites that are built for IE11. This is mostly needed in corporate environments with internal web pages that are coded for IE11.