TB Immigration Information Letter No. 051/23: Don't forget to put your e-visa in your passport when you renew

You will then have to show that visa every time as long as you use the same passport. Not just during the first extension. Although it may depend on the local immigration office, like many things.

But you can still apply for multiple extensions with the same passport. The number of extensions you can obtain with the same passport will depend on how long your passport is still valid.

I expect the same applies to a new passport as with the sticker, i.e. the visa details will be transferred to a stamp in your new passport.

Or of course they had to decide that now that you no longer have a sticker but a printed visa, your original visa should simply be transferred and you should put it in your new passport.
That's also possible, of course, but I don't really expect it and they will simply register it in the new passport with a stamp, as has always been the case.

This e-visa is fairly new and the future will tell what they will do with a new passport.

Also remember that it will depend on the local immigration office, as with many other things.

But given that the evisa is quite recent (only since November 21), there is not really much experience with annual extensions to get a clear picture of what usually applies at most immigration offices.
Ultimately, it will explain itself locally and as you say, it is best to have a copy with you in case the wind suddenly comes from a different direction.