you can find the serial number on the side, but a better option is to go into system settings. it's one of the last options iirc. it will say the serial number. it might be more prudent, since you can just replace the sticker on the side to fool someone. I'm sure that's what Nintendo uses when it comes to repairs too.
XA = v1 Erista
XK = v2 Mariko
XJ = v2 Mariko (Lite)
XT = v2 Mariko (OLED)
Only half of the v1 are vulnerable to the fusée_gelée exploit, which is why you have to check on ismyswitchpatched
But if the sn does not start with XA, don’t mind checking anyway