To answer your question directly: yes, it's possible to switch to the 4-button fob, but on the newer generation trucks, it is definitely more hassle than it's worth. You have two routes you can take here:
Option 1: The Easy Way (Keep your 3-button fob)
You don't actually need to swap fobs to get remote start from your keys. You can grab a plug-and-play module like the Ford Perimeter Plus security system (an OEM Ford accessory) or an aftermarket kit from a place like Accessorides. It plugs right into the harness under your dash in about 10–15 minutes. Once it's in, you just press Lock-Unlock-Lock (or Lock-Lock-Lock, depending on the kit) on your current 3-button fob, and the truck will fire right up. No dealer visits, no cutting keys, and no programming required.
Because your truck can already remote start via the FordPass app, your truck's computer is already programmed for it. That means you shouldn't need the "Ford Dealer activation" mentioned on that webpage. Once you plug the module in behind the OBDII port, the truck will recognize it and you can just use the Lock-Unlock-Lock sequence on your 3-button fob to fire it up
Option 2: The OEM 4-Button Fob Route (The Hassle)
If you are dead set on having that dedicated "2X" button on the fob, it's a bit of a headache on the 2023+ Super Duties. Because Ford locked down the security architecture on these newer trucks, you can't just program a new key yourself using FORScan like you could on the older models. You would have to:
Buy the correct OEM 4-button fob (and possibly swap out the RTM - Radio Transceiver Module in your headliner if your truck only came with the 315 MHz receiver instead of the 902 MHz one).
Get the emergency key blade cut.
Pay a dealer or an auto locksmith with FDRS software to program the immobilizer/PATS system so the truck recognizes the new fob.
Go into FORScan to manually enable "Remote Start" in the BCM (Body Control Module) and IPC (dash screen) so your climate settings show up.
Honestly, most guys in your shoes just grab the Perimeter Plus or a plug-and-play module. It's much cheaper and saves you the headache of dealing with dealership programming fees or tearing into the headliner. Hope this points you in the right direction!