CTRL + tab cannot be sent out by BTT

I am a 10+ year heavy BTT user. First, thank you for developing this fantastic app. It is the only reason that I stay with Mac.

I just bought a new macbook 16, buy a new BTT license for it, and import old settings. But, run into this problem:
in the "For all apps", I have two items (3 finger swipe right) and (cmd+k) that are supposed to send key combination (ctrl+tab) to switch to the next tab in most apps.
However, it is not working. On some apps, it functions as only "tab", on some apps it switches back to the previous app.

I check other apps, it seems that none of them can receive ctrl-related combination from BTT.

All other keyboard combinations (without CTRL) work fine. So the "security and privacy", "full disk access", etc related setting should be correct.

Appreciate if you may take a look of this issue, since I have so many shortcuts in various apps that use CTRL. Thanks!

So far I've tried:
in "privacy and security", add and remove BTT
in BTT setting, "Always use old keybaord shortcut implementation", "automatically switch to old keyboard implementation if secure input is enabled", "use higher level modifier key recognization", "add small delay", I've check and uncheck one/some of them.
change to the latest alpha version

I can’t think of any reason why BTT would be unable to send that shortcut, it sounds pretty standard. Instead I’d assume your issue might not be within BTT. Does the shortcut in general work for all the apps you want to use it with?