So I downloaded the 2022 F3 Operator's Guide from
https://www.operatorsguides.brp.com
On Page 64 in the section "Using the Audio Input Jack and USB Ports" it has a diagram of the "glove box" on top of the display showing the Audio in jack and USB jack.
On Page 41 it has this information about the Glove Box:
But then there's some bad news. No where in the 2022 F3 Operator's Guide do I see any mention of Apple CarPlay.
In my 2024 RT Operator's Guide there are 10 references to CarPlay.
The only references to Apple in the 2022 guide refer to downloading the BRP Connect App to your iPhone.
So it looks like your 2022 only supports BRP Connect/BRP Go. There's a link in the 2022 Operators Guide for information about BRP Connect/BRP Go:
www.brpconnecttutorial.com
That's a general webpage for all BRP/CAN-AM products, so you'll need to scroll down to the CAN-AM ON-ROAD link for more information.
I also downloaded a copy of the 2023 Operator's Guide and it has the same information about BRP Connect/BRP Go as the 2022 Guide, and no mention of Apple CarPlay. That corresponds to my understanding that Apple CarPlay support was first added on the 2024 models.
As to your question about a wireless CarPlay adapter, I don't think that will work, since all it does is eliminate the wired connection, not add Carplay capabilities to your display.
I think you're stuck with something like a Carpuride device mounted to your handlebars:
https://carpuride.com/
I would also suggest looking at Garmin Zumo XT or Zumo XT2 GPS models.