Sharing Android's Wi-Fi internet connection via... Wi-Fi. Not just extending!
You need a phone with 2 sets of Wi-Fi hardware built-in, so that one can be used to connect to your original one and one can share. Unfortunately those are incredibly rare - the only ones I know of are Huawei D2 and Samsung's S7 family.

In your case where your network requires sign-in, consider using your phone as a proxy server and set other devices to use it. Probably works, probably not, but it's the only approach I can think of.