Engagement photos

You could do them whenever, though that is a long time to be engaged. I've been engaged almost 2 years and haven't done them - will probably do them later this year or next year sometime before we get married

They're photos to mark your engagement so honestly any time during your engagement they are perfectly fine. I think more often than not they are done earlier/shortly after the engagement. My engagement went from 2.5 year to like 3.5 years (thanks to COVID) and we ended up getting our engagement photos done 2 years later. We actually weren't going to get them done but then because of COVID/having to postpone we said why not!

Anytime, really! I had a friend know she was doing a long engagement, so they got one set done right after (really just to celebrate!) and then another about 1 year out from the wedding to use for save the dates! Seemed like such a fun way to celebrate twice.
We have about a year and a half engagement and did ours about a year out.

Maybe think about what you would use your engagement photos for? If it's to announce your engagement, then you can do them soon. If it's to include in your save the dates, then you can wait until 1-1.5 years before your wedding date. If it's to get practice with your wedding photographer or included in your photography package, you can wait until you hire one (1-2 years before your wedding date). Or if it's just for fun, literally whenever you want!

I would do them now, since you are engaged. Who cares if you have a long engagement! That will give you plenty of time to prepare financially for this event.