I never used AutoCAD 2021, but I never had issues with AutoCAD 2020 (or any other version I used) using a wireless Logitech keyboard (K750). For a while I had issues with my Logitech mouse (MX610), but that was because the dongle needs to have direct line-of-sight to work well (I added a USB cable extension to the dongle and haven't had issues since).
I'm using the SetPoint software and driver. I've read Logitech's newer software has a lot of issues, but haven't tried it myself. I'm currently using SetPoint 6.67.83 with driver 5.90.41.
Work: AutoCAD 2022.1.3, Windows 10 Pro v22H2 64-bit, Intel Core i7-8700K, 32GB RAM, Samsung 960 Pro SSD, AMD Radeon Pro WX 5100, 3 Dell Monitors (3840x2160)
Home: AutoCAD 2022.1.3, Windows 10 Pro v22H2 64-bit, Intel Core i7-11700, 64GB RAM, Samsung 980 Pro SSD, NVIDIA Quadro P2200, Dell Monitor (3840x2160)