If someone buys you a drink

the problem is, the thankyou may seem like progress when it's the opposite

I'll thank them and chat, but I don't feel obligated to them.

If a person asks to buy me a drink and I have the opportunity to refuse, then I would say I would owe them the courtesy of talking with them if I accept.

On the other hand, if the drink just appears and the bartender points out who bought it, I don't think I owe them anything. In a bar, a "free" drink is usually an attempt to manipulate someone. (Not necessarily sexually. I have had windbags buy me drinks just so they can keep me there and keep talking and talking to me! lol)

If a woman buys you a drink, it means you're "in like Flint." 😎

If a random person was to buy me a drink I'd politely decline in case it was spiked/drugged in some way.

Like you I am not a bar person and have never been to bars/clubs/pubs with the express aim of finding women to 'pick up' for ons/nsa sexual encounters.

No one is obligated to do anything just because someone bought them a drink or even any other gift.

A thank you will do, or you could even politely say thank you for the offer, but no thanks.

I have always been the one buying and it has always ended up in conversation. But if they want more than that, I am good to walk away

Not necessarily but at least thank him for the drink

No. You are not obligated. Just signal or say thank you.

if they bride, no