Router bit without shank

I believe you may be mistaken, I see a collet nut and presumably collet nuts can be turned. It is very possible that the shank of the bit in it is stuck after many years.

I found the manual online Here. Page 3 shows the bit changing instructions.

Click on this link to download a PDF of the manual

I owned one, same model i believe, and it definitely had a collet and i could change bits.

Here is a YouTube video of a similar model being resurrected.

You normally shouldn't have to disassemble the collet to get the bit out, but perhaps it was necessary in this case -- the bit looks quite rusty. I wouldn't try to use that bit again, and I'd inspect the collet carefully; if it's anywhere near as rusty as the bit, it needs to be replaced. And if you're correct that the collet size is 10mm, you may need to replace it with a more standard size (preferably 1/2").

Ultimately, if you can't find a new collet that'll fit this router, you may need to replace the router. No matter how well the motor runs, you don't want razor sharp carbide spinning at 25,000 RPM without being held very securely in place.

Are these types of router bits still sold?

I doubt you'll find new cutters to fit that old shank, unless it's new old stock. There are some bit sets where the cutters are separate from the shaft, but in every case I've seen the idea is to change the configuration of the same cutters, not to completely replace the profile. For example, [this cope and stick bit] has two cutters whose positions can be swapped on the shank to cut mating parts of the same joint.