One of my Expert Devs, Matt Daniels, created a module you can download and implement to log people in without it forcing them to logout and back in upon account creation (not visibly): https://www.mattkdaniels.com/blogs/walkthrough-enabling-autologin-functionality-within-your-mendix-app
The problem might be that Mendix is designed in such a way that normal and anonymous users are by default not allowed to change accounts of other users. Preferably you want to keep it this way and don't change anything in the security settings on user account mangement.
A user can only login with an account which is a (specialization of) System.User object.
My approach would be as follows:
If you would like to have the users automatically being logged in after creating the account, you would have to revert to custom Java and a Custom Login handler. For more information on this, although the blog post is pretty old, it still applies: https://bartgroot.nl/mendix/custom-checks-on-login/
Hope this helps.