[HemiLonestar]

So a 2016 year of "the same engine" is not the same engine; the only thing they share is displacement....maybe starters and oil pans. Two very different engines.
Can it be done? Yes, and has been done. Smooth? No lol. Your PCM will absolutely not run that engine UNLESS.......you swap to a 32T tone ring and lock the VVT. Then you can just custom tune it, however you negate the whole advantage of using a VVT engine; then it's just easier & cheaper to cam it or cam it with better heads and you'll make the same power or better with less hassle.
The normal method is to get a 2009-10 PCM (newer 08-10 CAN style, but still within the same basic platform) with harness alterations. You'll need the front accessories, etc from an 09-10 5.7 becaus ethey changed in 2011, plus the 2016 engine doesn't have a PS pump (which you will need and your stocker won't work).

 

[HemiLonestar]

See, I more got this engine because I was able to get it for 1500 which saved me so much more money so I could afford to get the labor done properly. I don’t care about power right now, just so long as I’m not putting in like a 2.7 or something, I was just trying to match the power as best I could for the price. So if I were to take it to my mechanic, would you say I’d only need to purchase a 32 tone ring, the front accessories from an 09-10, and ps pump? I would get an 06-10 since they are almost the same model, but the cheapest I could find a used one was 3000. This is more just trying to get this car running again till I can fully fix it up in the future. Any other tips or advice if that changes anything?

Keep in mind, it isn't just "swapping the tone ring"; the crank has to be pulled completely OUT to do that.
Accessories from an 09-10 will have a PS pump already.
It isn't 06-10, it's 05-08. From 09 on it's the eagle engine.
If you're just "trying to get it running" then you bought the WRONG engine (no one researches anymore, they just see dollar signs lol). Find any 05-08 5.7 car engine and drop it in. Plug and play.

Also, would the PCM from my old engine work if I keep it in there? I know I’ve seen people do it and then tune it but I know i haven’t done it before so while I’m asking about the other things.

Go back and reread my original post very slowly.