Try this logic.
If user not signed in(check with tingDB) redirect to sign up page.
On successful login, store sign tinyDB with some value and store the detail in google sheet with username as email id or phone number
Next time user while try to login with username (may be of email id or password) call that data alone from gsheet using gviz method..
If value is matching with password login and open next screen.. if not matching or no value found alert user with text
V Simple
(Use script to store data to gsheet but to retrieve data from gsheet, no need to script for the exact cell value alone)