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Does your HDMI cable also have "lags and disconnects"? I mean, when you have hardware compression (presumably?), it's not all that different to send it over HDMI than ethernet.

Compression latency should be in low milliseconds (1 ms should be plenty.) The latency over ethernet is going to be measured in hundreds of microseconds. Sending a compressed 100 kB frame over it takes 800 microseconds, which can partially overlap with compression. Noticing 2-3 milliseconds extra latency is going to be pretty hard.

Something is badly wrong with your setup or with Steam Link.