dont show cache for logged in users

when this option is checked the logged in users are shown fresh content that’s correct but how can I limit this rule only for homepage dont show cached homepage for logged in users

this is because I use modal login popup of Digits plugin which uses OTP for login but after successful login, the login button doesn’t change to my account button and also logout button doesn’t appear but this happens only ono homepage not on other pages

I want my websites to show cached version for logged in users also except homepage

that means all users will see cached homepage but when user login then the homepage that will be shown will be fresh