The AV1 codec has support to tell the decoder to generate fake film grain, so you can add back all the noise lost in compression.

Although I don't think it's very widely used, I dunno if that's due to the compressors or decompressors.

It needs to be done by the client and not be part of the actual video stream, otherwise it doesn't even work. When done by the client it's cheap.

Not so cheap if your hardware decoder only supports 8-bit color, which is a common limitation of H.264 decoders in particular.