as no new features are being added to the .net 4.*, if you want to move off web forms you should pick asp.net core, otherwise you would need to port again to get new features.
the suggested replacement for webforms is razor pages, but it a template approach rather than a component tree. If you want a component approach, then blazor may be an option.
if you think the port will tale more than a month or you can wait a month to start the port you should pick .net 6 (in preview now but release is scheduled for nov 9). .net 6 is a LTS version and has longer support than .net 5 (whose support will expire in 4 months).