Oh ho ho. Paint gets very brittle as it ages, and this my friend is an aged frame. Good for you for keeping it going.
There is no question in my mind that in fact the headset they installed, smacking it in with a plastic mallet or a press, was a very tight fit indeed, in fact I'd guess it really didn't fit too well.
There were two solutions: hone out the inside of the head tube, or grind down the new headset, the first of which requires tools, and the second requiring a knowledge of machining.
They definitely popped the paint off. That paint's been on a long time, and the only way it's coming off is if you stretch the metal underneath, or take a screwdriver to the paint...and it would be a tough scrape indeed.t
Solutions? At this point I'd be concerned that the head tube may even be cracked, can you imaging how much poundage had to be put to the bottom race to get it in the tube...enough to distort the metal.
A pro painter can probably repair this pretty well, but duplicating the exact look of the original is hard indeed, and pricey.
I did museum quality motorcycle renovations, and this is a tough fix.
Look at the safety issue first...take it to another mechanic for a review of the condition of the head tube, if they bent it or cracked it, the frame is junk.
If the metal is just stressed, and stretched a bit...you are likely ok.
You can buy a replacement frame of this type for less than the cost of painting their error.
You would be amazed at the horrible repairs I've seen from quality shops over the years, by pros, especially in the motorcycle world.
This reminds me of a story when I was head mechanic as a kid at a bike shoppe.
First day, the owner showed me a dented frame, "Repair it and repaint it," he told me.
Bent frames are trash, "I'll strip a replacement frame off a parts bike I told him."i
Damaged frames are junk.
Also...how does the new headset work...smooth, no binding? Take off handlebars and wheel...can you spin the fork through 360 degrees of movement...any binding at all?
Pretty is as pretty does.