The backgrounds are indeed bitmaps, stored in .TIM files on the disc. It is likely that the BGs and sprites for the ads are located in the .BIN files on the disc as well. The problem is, no matter what program I throw at it to open the .BIN files, the thing won't work (even Game Extractor fails me). Oh well.
Naulahauta would be the person to speak to about this. Let me see if I can raise him.
So anyway. Bored and sleepless this morning I had a little dig around re: neural net image upscaling, and it turns out that yes, there are now tools available that don't require installing a mess of Python packages, then compiling this over here, nobody got time for that nonsense. A bit of messing around later, I have to admit I was pretty blown away, just look at this:

That's bloody witchcraft, that is. Full image comparison
here. The original I used is attached to this post, in all its 33Kb GIF glory. I did have a bit of a dig on Google to see if the backgrounds were available elsewhere, ideally in a lossless format, but I drew a blank (dead links), so keep plugging away if you can! If anyone else has these backgrounds, or the original file of the in-game ending anime video from Shun, please upload it somewhere. It's neat to see those photo backgrounds with a newfound clarity.
I also did some of the advert images you provided, but they are one seriously mixed bag using this technology... The cup and sweets came out lovely:

However, Kawase herself fared really badly. If you want a visage of a "4th degree burns to the face survivor" Kawase to haunt your nightmares, click
here.
There are other neural net tools for video. The one I've tried was supposed to use my GPU but didn't, and thus was excruciatingly slow. I'm going to keep trying to get the GPU processing working, maybe it would be possible to tidy up that Shun video. There's also a VHS-ripped advert for Shun which might benefit.
Also, the problem with Paint is that I use the bucket tool to get rid of all the black around the sprites. The thing is, it leaves some of it on the sprite itself. I'll take your advice for trying Paint.net though.
Yeah, Paint.net has a simple brush tool called "Recolour" which will deal with those wrongly-coloured edges in seconds.