You will want one with HDMI pass through though. Like this one https://www.amazon.com/Mirabox-Passthrough-Nintendo-Streaming-Recording/dp/B08QJ84JNP/

Or if you really need as cheap as possible, some get even cheaper...https://www.amazon.com/TreasLin-Capture-1080P60-Latency-Pass-Through/dp/B08Q7CG9PZ/

Given those specs, I suspect it's a rebadged generic HDMI capture device. Those can be found for $10-$20, but most are USB-A. (Here's a $15 USB-C one.) I have no clude if they work with M1/Apple Silicon Macs.

(I should bring up that there have been reports of these cheap capture devices overheating/failing. I don't know if it's a specific model or form factor or what.)

MiraBoxes might be different chipsets/manufacturer since they claim to support 1080p60. Supports USB 3.0 and I guess a USB-A to USB-C cable could work. Seems to be about $40. (And there's a TreasLin capture box that seems to be the same device, but only $20 with coupon.)

For $60, you can start to find higher grade capture devices. AVerMedia Live Gamer Mini Capture card is $70 on Amazon, but's it's USB-A and again no clue about M1 support. AVerMedia ExtremeCap is $80 and supports USB 3.0, the 4K version is $87 (these apparently are USB-C).

For $90, there's an EVGA USB capture card, the EVGA XR1 lite. No clue if it works with Mac OS X/M1. (An Amazon feedback/review apparently got it working with an M1, but it didn't record chat or something.)