Another post mentioned just giving cash anonymously and I think that’s easily the best option. You would almost certainly have access to their mailbox if it’s a suburban stand alone type? If not, an unmarked envelope under the door, with cash, would preserve plausible distance from making the neighbor feel like they have to decline out of etiquette.

Don’t think about it more, they clearly need the help if they mentioned it, and if you can help without feeling the impact just do so without strings or direct attribution. They’ll suspect it, and can if they approach you in genuine thanks if they want, then you’re able to be gracious about accepting, or simply act surprised and happy that such a nice thing happened if not.

I’ve had people clearly embarrassed at the grocery checkout take a 50$ bill I claimed fell out of their pocket before several times. Preserves their dignity even if it’s just a pretext for helping. Puts the ball in their court at least. “Hey man, I don’t know what to say but it’s not mine. Pay it forward for someone who needs help if it’s not yours” is the worst that’s ever gone for me before. Nobody likes being a charity case.