When I googled Nokia 2720 Flip, the results I got were not a smartphone. Am I missing something with that device?

The only two big names in this particular folding form factor right now are Motorola and Samsung. I don't think you could go wrong with either one of their most current models (Razr Ultra and Z Flip 5). I personally have the Flip 5 and prior to that owned the Flip 4.

Some differences:

Samsung does fantastic yearly trade in deals if you happen to live in the US. I paid only $50 to upgrade my 4 to the 5. Motorola doesn't tend to have deals this crazy to my knowledge. And Samsung does not have deals like that outside of the US either.

The Razr is slightly larger than the Flip.

The Flip takes slightly better photos and videos than the Razr.

The Razr has a dust resistant rating (but is not rated for water submersion) whereas the Flip has a water submersion rating (but is not rated for dust)

The Razr comes in a bolder color than the Flip.

Both have a great cover screen. The Razr's screen is technically slightly larger than the Flip, but the useable screen real estate on both is actually very similar due to the camera cutouts.

Samsung has more bloatware on their phones. For whatever reason, they insist on making their own messaging app, gallery app, notes app, calendar app, etc. Meaning if you migrate over to them, you will often have two of many base apps. Luckily you can just hide the ones you don't use.

Both phones don't have fantastic battery life compared to other flagship phones, but I can usually easily last a day without needing to charge personally.

Both phones have a slightly different implementation of how the cover screen works, but I think they both work fine. The new, larger cover screens on both devices has been a game changer. If you get the Flip, be sure to install Good Lock (a free Samsung app) to unlock the full potential of the cover screen.

A YouTuber recently did a comparison of manually folding and unfolding each device head to head for many days until the hinge broke. The Razr lasted around 140k folds and the Flip lasted significantly longer at 400k folds. Keep in mind that this isn't a wide scale test. But reviewers have commented how the Razr's hinge makes a bit of a crunchy noise and the Flip's is essentially silent. 143k is still not terrible. If you fold your phone 100 times a day, that's still quite a bit of time with your phone before the hinge breaks. But it's worth considering.

There is another brand, Oppo, who makes a phone in this form factor. But the cover screen is small and I'm not sure if it's only available in China. Either way I'd steer clear.

Something to note is that yearly maintenance with the phone will be changing the internal pre-applied screen protector, as it will eventually lift at the crease. It's really not a big deal imo.

Then there are the phones that unfold to become mini-ablets. With these, you have companies like Samsung and Google trying it out. I think maybe a few more companies, but I tend not to follow this scene. I don't really have a use for a chunky phone and mini-ablets, personally. They also are more expensive than things like the Razr or the Flip. But some people love the form factor.