I have used 2011 MBA, 2017 12" Mb, and a 2019 16" MBP that all used intel chips and also did not have these issues with Bluetooth. I have even used windows laptops in the same configuration at the M1 MBA that did not see the level of lag and choppiness.
Apple even released an update specifically for M1 Macs to address Bluetooth issues. I'm pretty sure there is an issue somewhere with the Rosetta 2 translation of Logitech Options or Logitech software, or Apple's Bluetooth chip is somehow not up to par with intel configurations.
Again, I love Apple, but I was there when everyone with an iPhone 4 was dropping signal because we were all "holding the phone wrong". Sometimes, there really is an issue.