That would be where I'd look first. A lot of AIO manufacturers only write drivers for Windows. There's an old Reddit thread that has a few things to try. If this is your first dip into Linux get used to googling things. A lot of things. Ubuntu or Kebuntu are great OS to start on because there is always a forum post or a Reddit thread that deals with exactly what you're dealing with. Once you are more comfortable I'd move onto Linux Mint or straight Debian. All those nice things that make Ubuntu easy to learn will eventually also hold you back.

Do you know what model AiO you have? Some models report pump speeds as higher since they have multiple magnets triggering the RPM sensor, so the 1600 might actually be 800 or even 400, which is way too low for the pump.

I would try setting the pump (and AiO fan) to 100% speed in the Bios for testing. Some pumps work well with a fan curve, some don't.

Edit with more technical details: Normally each revolution should generate 2 Pulses on the rpm Feedback wire. But Pumps don't always follow this spec so might over or underreport their actual rpm.

If your AIO pump came with a hub you likely need to use it instead of plugging directly into the Mobo.

As an example my corsair AIO came with a hub and i didnt want to use it. Finished my build and found out i absolutely had to use it in order for the device to work properly.

Look up CoolerControl I use it for my Corsair AIO, and my CPU cooler runs entirely off a USB header. But CoolerControl also supports motherboard headers.

You can use it to make custom fan curves and check pump/fan speeds.