I would try disassembling and cleaning everything.

The anti-glare coating doing that was very common for that era of LCD screens.

I have one of the tiny Sony laptops that had that issue with the screen and you can remove the coating by taking it out of the casing and laying a damp washrag on it and letting it sit for a day or two for the first iteration.

It should turn quite a it of it soft and you should be able to remove some of it.

Then you do the same thing again and again until you get all of it off.

You will want to be super careful because the glass under the anti-glare coating scratches really easily.

Once you have it all off and hopefully have not damaged the screen, you can put a large tablet screen protector on the screen. Just search for similar / larger sizes and then cut the one you get to the correct size.

Yes, it does take some work but it can be worth it over trying to find another good screen which will also end up having the same problem not too far down the road.

The white powdery stuff is what happens when magnesium corrodes - that's what that internal frame is made out of. It was likely caused by the off-gassing from the vinegar syndrome screen. If the laptop powers on fine, then I'd definitely say it's worth restoring. The bad layer of the screen isn't an anti-glare coating, it's the polarization film. You can peel the remains of the damaged film off, and then remove the adhesive left behind with isopropyl alcohol. Then you'll need to find new film of the correct angle and apply it down - application of the new film is the hardest part.
As cyclone3d said, the work is worth it as a replacement "good" screen will develop this problem at some point. Replacing the film instead will give you a good 30 years or more if you store it in good conditions.

The replacement film I used was simply a matte anti-glare screen protector.

Had no idea I needed anything else. It just worked.

Update - I finally had time to disassemble the whole laptop and the corrosion on the casing is horrific, as seen in the attached photo. The marking seems to indicate it's made from Magnesium AZ91D Cast Alloy: https://www.azom.com/article.aspx?ArticleID=9219

Any suggestions on how this could be cleaned? I'm afraid white vinegar will react strongly to the magnesium so I'm reluctant to try that.

Once it's cleaned, I would also like to use some sort of sealant to prevent further corrosion.