you can write web service that call the signin api. with a web site, the code sets a cookie, but this will not work with a Maui app. Typically you would use a bearer (jwt) token instead.
you don't say which framework you are using. the solution will depend on which framework you are using, but the aspnetusers table suggests the old mvc 3 membership. Hard to even find docs on this anymore. You should really take this opportunity to upgrade to the current identity system. any to add token support, you will need to override the onauthenticate event in global.asax and add support for a bearer token.