In macOS setting, I have "Automatically hide and show the menu bar" setting as "In Full Screen Only". I run Windows in full screen mode with this setting. On Windows (full screen mode), if I maximize browser (Chrome and Edge) then I cannot drag a tab when I have multiple tabs open in the browser. The issue does not happen if I change "Automatically hide and show the menu bar" setting to "Always", "On Desktop Only" or "Never". Does this happen to you? Can someone confirm?
I observe the same behavior. I found I could drag Chrome tabs running in Windows full screen mode with the "Automatically hide and show the menu bar" option selected in the macOS by going to Parallels Settings -> Options -> Full Screen and checking "Optimize full screen for games." Chrome isn't a game, but this made it work for me. Give it a try!