Thanks for your input. It manages to remove the noise with DSP Bypass mode but not True Bypass mode, so I reckon it's the DSP bypass only. I can't find any information about that anywhere. I can't see a noise gate in the setup. And yeah, I'm not using the dedicated noise gate effect (under Distortion, I think).
I want to get a really small, really cheap pedal to do what the DSP Bypass mode is doing. I don't want to get another Line 6 M5, just because I don't see the point in getting something with so many features that I don't really need. For example, maybe the Mooer Lofi Machine would do the same noise removal as the M5 if always on with dry output only? To know this for sure before I buy one I'd need to know what DSP Bypass mode is.