The answer to this is simple: they're different generations of trackpads.
For a little history...
The force touch trackpad debuted in the early 2015 MacBook Pros (and the 12" MacBook) with the gen 1 trackpad. On the original version, they could not design the haptics to generate the clicking sound, so the haptic motor only simulates the feel of the click, while the clicking sound itself is generated by a piezoelectric speaker inside the mechanism. The same type of speaker was used in prior iPods to simulate the wheel clicking sound.
In 2016 when the MBP's were redesigned, they came out with a 2nd gen version of the trackpad. The haptics were redesigned to actually generate the click sound as well as the feel. Generally this generation makes a deeper, fuller, slightly quieter clicking sound. I've also found it to be a weaker clicking feel, at least on the 13" models.
The 2018+ redesigned MacBook Air uses the original gen 1 haptics. I imagine this is because they pulled the design directly from the 12" MacBook which also did not have much space in the chassis below the trackpad, unlike the Pros which have a lot more space for a beefier mechanism.
This is all to say, your 2016 MBP had then gen 2 version, and the 2020 MBA has the gen 1 version. The gen 1 has a sharper, higher pitched click to it. But, on the plus side, unlike with your prior MBP, you can turn on "silent clicking" in trackpad settings to decrease the volume of the click. That's because the gen 2 version made the click with the mechanism so the sound literally cannot be turned off, while the gen 1 again makes the click with a speaker, so the setting is available to turn that sound off. I can see though that you've done that and you're not satisfied, unfortunately, there's nothing else you can do. You either get used to it or you switch back to a MacBook Pro.
