Plenty of good hints from Wilkinsonwilfrid there.
For AH Voice, check if you have other apps that use your microphone running in the background, including Edge and Copilot. Also shut down any voice apps that may use the same keys to trigger the microphone. Further, if there's a software included for your new headset, any voice enhancing systems can cause some input delay not to mention the ones that make you sound like someone else.
And finally, especially if you're playing other games with communication ability, do a Restart for Windows before starting a new game. Restart (not Shutdown and normal start unless you keep the Shift button pressed while clicking Shutdown) will clean all settings so there won't be any leftovers interfering in the background.