As they’re handmade (but not in the recently created handmade category) they have no "CE " mark, or anything like that. Is toys and games no longer suitable?

This is undoubtedly the problem. You are making handmade toys but selling them in the general toys and games category. All toys in that category have to be CE approved, it is European law. As your items are handamde, presumably they don’t have their own, pre produced packaging? I also presume that your products meet the European standards on toy safety? Even in handmade, toys still need to meet these requirements on product materials, paints used etc. So, your toys have obviously been acceptable before but it appears now, Amazon are getting more strict on what can be listed and where. Is it therefore likely that you may need to switch to the handmade category instead for your own products?

As for any others that you sell, which you don’t manufacture (and we are toy and game sellers), the images you are adding have to show the CE mark and you have to show all sides of the packaging, in enough detail so that any wording can be read. This issue has appeared before on the forum several times from sellers having similar problems.