Hi Colin,
The SE 2020 is one of the last iPhones that does not have a serialized screen, meaning it is not paired to the logic board so you won't get that bogus genuine parts warning if you change the screen.
However, all phones that support True Tone (that is, all phones after the iPhone 8) need to have a piece of data called the MtSN copied from the original screen to the replacement in order to keep the True Tone function. A device programmer is required to copy and reprogram the data; both the JC V1SE and the QianLi iCopy programmers support that function. Figure on spending at least $85 USD if you want to buy a programmer for your one time use. There's always a chance might be able to find a local repair shop who can do the programming for you, but that's a crapshoot.
Otherwise yeah, @thequacker is absolutely right that you do have to swap over the home button or you'll lose your Touch ID function. If you don't use Touch ID then you can just swap over the screen, but I'd suggest holding onto the original in case you ever decide to sell the phone; you'll get a much better price with the original home button.