The box is called an "audio processor", but in my usage, all I care about is a compressor/limiter. For a mic, probably also a gate. You can get those functions pretty affordably, here's an example I found with a quick search:

https://www.sweetwater.com/store/detail/MDX2600--behringer-c...

This isn't really my field of expertise so I can't recommend specific gear. I suspect you could do it with a PC/SBC but latency would be a concern.