I have discovered that some SPFx client web parts don't work the same on classic pages as they do on modern pages. I'm currently working with the SPFx Fantastic 40 WebParts. If you try to use the Accordion web part on a classic page, you cannot edit the text, but if you deploy the same web part to a modern page, it works without issues. Is there any MS guidance on what works with the classic pages versus what works with the modern pages?
There is nothing particular. Most parts should work fine, but need to be tested and validated. The SPFx Fantastic 40 isn't developed by the product team. There might be some assumptions made in the F40 code around modern pages that don't translate cleanly.
Are you seeing any errors in the console or the network tab? Might be worth logging an issue in the fantastic 40 github issues list.