I must admit that even with 15 years of experience with WordPress I have never put WordPress into maintenance mode manually, I've always used a plugin. Using a plugin will allow administrators to log in during maintenance mode and work on the site.
Considering this is expected behaviour I question how useful this function is. WP is put into maintenance natively once a update is processing anyway, so it renders the Enhance maintenance function useless. The main reason to put a site in maintenance mode is to be able to work on the site while it's closed to the public.
Please keep in mind that most users would expect to be able to log in and run updates from the WP control panel. Enabling maintenance mode in Enhance does not allow that, the only option is manually via FTP/SSH or by SSH/WP-CLI.