In the tg chat, the admin offers to log in to the wallet on a third-party resource, allegedly this is necessary to verify the crypto wallet. They ask you to enter a SEED phrase. I don't know what to do about it
You are most likely being scammed.
Seed phrase would mean the wallet's seed phrase, which is should NEVER share with anyone, because doing so gives that person access to your coins in that wallet and they can spend it at their own will.
I am not surprised this happened to you on telegram, scammers are often posing there in different names and personas to fool users and steal their money. Possibly they are not even part of the casino you are talking about.
Can you give us some details as to what happened step by step?
Also do not share any personal info with anybody or God forbid, your seed phrase.
EDIT: I read your edited OP again, it seems you are a victim of the old skool method of where you are shown big numbers on a site and when you ask for withdrawal you are asked to pay for that deposit. It is an entire scam because you actually have not won anything there and the numbers are fake. Whatever you pay them to allow your withdraw is going to their pockets, they will never let your withdraw anything.
Please move on to another legit casino.