yep, I understand that. sorry, I don’t know of a peer to peer way to work with bitcoin....hopefully others in this ping list do.
“ I had to provide them with my BANK LOGIN ID AND PASSWORD as a funds verification step.”
Hard to transfer $ to buy or back into your account after you sell without it.
Couldn’t you just change your bank password after verification?
Make sure of the site by checking the address. Watch out for spoofing or fishing attempts if you decide to proceed and change your password immediately after you've connected your account. Also use two-factor identification.
There are other ways to move funds. Maybe a wire transfer would ease your fears? Or perhaps fund your trading account using a credit card to purchase crypto through coinbase, then move the crypto over to their trading platform.
Driving this is the KYC laws. I've had a coinbase account for a long time, and don't recall the need to do this to link accounts.
You're wise to be cautious these days!