Where you're going to run into issues with what you're looking for is screen size. The days of Flagship phones being <6" are gone and that's were they're putting those premium batteries.
I think you should rethink your specs in the following way;
-6" screen - this isn't hard to find. The Galaxy S10e and maybe the S10 have the smaller form factor. The Pixels as well.
-Long lasting battery - 4000mAh may sound impressive but really it doesn't matter the size if the device isn't managing the battery well. So that really just ends up being a number, especially when what you really want is a battery to get you through the day. The Duracell phone has something like a 7000mAh battery said to get the average user through 2+ days but it's a brick of a phone if all you care about is a number.
-NFC - you'd be hard pressed to find a device these days that doesn't come with NFC. Actually I think it would be harder to find one that doesn't vs finding one that does.
-A good camera - well good is in the eye of the beholder. Look at all of the Apple vs Android camera comparisons. You can watch 6 reviews of comparisons for the same two devices and get a split decision in favor of either. So that might be where to start, is watching comparison videos on YouTube and seeing for yourself which device offers the look you're going for. Many people will say the Pixel 3 has a better camera than the Pixel 4 and that's between two generations of the same device.
-Nothing that has finished it's update life - well you're right on that one, anything older than 2 years has likely seen it's last OS update and may only get security patches for another year at best.
Honestly it sounds like you want an Apple phone...
You didn't mention pricing but hinted that an older model may work for you so I have to assume that price is a factor, but we have no idea where to draw the line.
The Pixels have everything except maybe the best battery life. I've seen some complaints about that, but fit everything else you're asking for at a lower price.
The S10 and S10e fit all of the things on your list if you break them down as I described without putting hard numbers on things, but you'll pay more them, even at a year old.