Contracts through Upwork aren't employee/employer relationships, so I'd be very careful about anything that suggests otherwise. If you have any doubts at all about the contract, either ask a lawyer to look at it or walk away.
It's fairly common for clients to require NDAs to be signed, but beyond that, not so much.
The payment method not verified isn't necessarily a red flag, but combined with a contract it's starting to edge in that direction. Ask them to verify the payment method before you accept any offer, and make sure that offer comes through the Upwork system - it'll show on your Proposals screen as a pending offer.
If they are asking for any personal information beyond basic contact info or asking you to handle money outside of Upwork for any reason (supplies, equipment, paying other vendors, etc.), walk away.
And be aware that communicating outside of Upwork before you accept an offer through Upwork is no longer permitted under the TOS.
If you haven't done so, read the material in the pinned thread at the top of the New to Upwork forum.