Do I need to transfer my non-B visa to a new passport before applying for an extension in Thailand?

If you have an actual visa, you cannot transfer a visa. Still, you need to transfer your current entry stamp before you apply for an extension.

If you are on extension, you have to transfer stamps to your new passport.

Now if you can do it at the same time as your next extension or not? It's possible.

But you are supposed to transfer your stamps to a new one immediately after you get your new passport. If the immigration officer thinks you take too long to do, be ready to be grilled about that.