You select the payment method when you make the offer. There is a link to change the payment method (and also your shipping address) from your default on the confirmation screen.
Buyers cannot opt out of the pre-authorization/"automatic payment" process. That would defeat the purpose of the program (which is NOT to make checkout "smoother" or whatever else the PR types are trying to spin it as this week).
eBay had been "experimenting" with requiring pre-authorization of payment for Best Offers for over a year and a half (started prior to Halloween 2021), adding more and more users into the test group required to do so (sellers can opt their listings out of it; buyers cannot opt out once they are assigned). Too many users were making offers and then not paying when it was accepted, and too many of those were scammers who would try to get the seller to text or email them to get their number/email address to send fake payment messages to.
They have now officially made it permanent and all buyers are now required to pre-authorize payment for Best Offers they make on listings for sellers who have not opted out of the program. They started trying it out on auction bids (with a smaller group of buyers that is growing) in Spring or early Summer 2023 and that is still experimental. They will also start experimenting with requiring pre-authorization or payment for accepting offers from sellers soon.
You can try to find a seller who opted his/her listings out of the pre-authorization requirement for what you are trying to do (bid and offer are two separate opt-outs). Unless s/he says s/he has in the item description you'd need to actually try to bid/offer and if it goes through without you having to add or confirm (with links to edit) your shipping address and payment method then s/he has opted out (or if a bid then you haven't been put into the group of buyers required to pre-authorize to bid).
