Is this frame too small?
 

My ideal size for a frame is 55-56cm. I found a frame I really want that is a 53.5cm. Should I consider it too small and forget about it? The top tube on it is 55cm and if needed, I could always get a longer stem- so no worries there. It's just the seat tube I'm worried about.

Why are you worried about the seat tube? It's the seat post you might should worry about. If it's too short, then you may not be able to get the extension needed from the seat tube for the saddle height you require.

A lesser issue for seat tube length might be that your bottles might need to be short. But not knowing all the other geometry of the bike, it's hard to say if that will be a issue. Just like it will be hard to say if your fit to the bike will be a issue not knowing all the other geometry of the bike. As well, what things you seek from the bike and how you ride most of the time. Hard and demanding or more relaxed.

I've ridden 64, 60 and 59cm vintage bikes all comfortably. And currently ride a modern 56cm bike.

It doesn’t sound like an unworkably too small frame. Shorter top tube length can be mitigated by a longer stem. A smaller frame (presumably measured from BB to top tube) will mean a taller seatpost and a greater saddle to bar drop. You can mitigate this somewhat by adding spacers and playing with the stem angle. What sort of spacer stack and stem angle are you currently running? All things being equal, you’re looking at another ~2 cm of spacers to maintain your current saddle to bar drop

Compare the stack and reach between the potential bike and what you like.
If the potential bike works, then buy it.

Nobody here knows if it will fit you, based on the info you provided.

You need to worry about the head tube also, to determine if the height of the stem (in addition to the length) will be adequate for what you want.

My inseam is 32.5" and a frame in the 54-56 range with horizontal 55 TT works well for me. Several years ago I bought a CAAD 12 which was labeled a 52. But, actual measurement is a 53.5 frame C to C. It fits me nicely.