When a customer tries to login to the front end website, they enter their user name and password and then when they click to login, it appears to be successful but they were not logged in. This is a fairly recent issue and I'm not sure what caused it. One possibility is that it's related to an update to my theme.
I had the same issue.
In my Magento 2.4.6-p2 I could not log in as frontend user, but I could see that its logged in as a user in admin area (Customers > Now online). It turned out, in Configuration > General > Web > Default Cookie Setting -> "Cookie Domain" field was wrong.
In first sight it was ok, something like "us.blabla.localhost", real localhost domain that I was using for local development. But it didn't work. So I changed it to this one ".blabla.localhost". Without first part of domain "us" but with the dot at the start. And after that it started working )
Hope it will help someone