I just got a frame powder coated and the people who did the work didn't coat the inside of the seat tube where it grabs the seat post. Does that matter? It had been painted originally but of course a lot of the material had worn off. As of now, I have nice, clean sandblasted steel. Thanks!

Probably better that way - grease your seat post when reinstalling and you should be ok. Or search for “framesaver” - I’ve never used it but lots of folks seem to like it - kind of an inside rustproofer.

It look like you got a good powder coater. If they did paint inside the seat tube, you would have trouble getting the seat post in. As posted above, grease the seatpost.

Yep, they did you a favor. If you do end up with powdercoat inside the seat tube, acetone on a cotton cloth will make short work of removing it.
Powdercoat left in the BB shell can be removed with a brass wire wheel and a drill.

The item to watch is right at the edge of the powdercoat- that is vulnerable to rust entry from the raw medal- grease will of course help.
But, keep an eye on it.
Any sharp edge on the frame is at risk, it is the physics of the semi liquid state of the coating.