I have tested according to the steps of first reply , but found that after disconnecting the session, when the login page is redirected, the system will immediately require identity authentication, which cannot meet your need. Maybe my test is incorrect. If there is a Demo, it will be perfect.
I have an idea for your reference:
add services TerminateUserSessions of CurrentSessionInfo
add button in logout mashup and add link in login mashup
So far, you can achieve the following: After clicking the button on logout mashup , the session will be disconnected, while the authentication will be bypassed, and the page will jump directly to the login mashup.