The RC522 sadly has infamously terrible range with x-series implants, as discussed a few times in this thread:
For easy Arduino integration, your best bet is probably a PN532 board, specifically the elechouse version:
https://www.elechouse.com/elechouse/index.php?main_page=product_info&cPath=90_93&products_id=2276
I’ve had some decent luck with knockoff ones off of Amazon, but other people here haven’t been as lucky.
If you are willing to gamble with a cheaper one, here’s the one I tend to buy:
I’ve had a decent success rate, and upon close inspection, the PN532 chip itself on my boards appear to be genuine.
The PN532 chip has some really great and easy to use Arduino libraries, mainly the Adafruit one. It took me less than 5 minutes to have mine spitting out UIDs to a serial console.
I’m not 100% sure that it’ll read through a windshield, but I’ve had decent luck through thick-ish plastic, without having to carefully position the implant or anything.
I’m not sure about the LF side of things with arduinos, the options seem far more limited from what I’ve seen. I’ve got 3 implants and only one of them has LF, so I haven’t looked into it too much. The xACv2 reads it decently well, but that’s more meant as a all-in-one solution.