3dscapture.com

If I plugged my 3DS into, say, a wall sockwt with the USB-C port from the capture card, could that break the card? Because it's able to charge the 3DS, and I don't want to break it.

No, that won't break it.

Is there a limit to the wattage like if I use a 45w charger will it harm the 3ds or is it fine as long as it's 5v

Most chargers worth their while today have a “transformer” inside that detects the safe wattage a connected device needs and limits the output to ensure it doesn’t pump more than that in.

I’d say just make sure you avoid any dirt cheap dollar store chargers or stuff from AliExpress/Amazon that have janky no-name branding and you’ll be fine. I’ve used a RavPower and Apple charging brick and had no problems.

Ok great, it's an Anker charger so I'd assume it'll be fine to plug into