I've been having some issues with certain apps not working with the "Move Window One Space/Desktop Left/Right" shortcuts. Specifically I've noticed this with Slack and most JetBrains products. Interestingly just clicking on the menu bar and pressing "Ctrl+Arrow button" also does not work for these apps, unless I slightly drag the menu bar a pixel or two first with the mouse, then
that system shortcut consistently works. If I click and drag slightly before triggering the BTT shortcut it also works.
So far I've only been using this with a Logitech Master Mouse 3 and an external keyboard (I don't ever use the laptop with the lid open), but it seems to have the same issues there in any case. I currently have a Macbook Pro 16" 2021 with a M1 Max running Ventura 13.5.2. I'm running BTT 4.306, but I've seen this behavior consistently over the last several months across multiple versions of BTT. Honestly I don't think this is an issue with BTT directly, but it seems like something happened on the Mac side (I don't recall if it started right after an update, but it could have). Regardless I think this may be solvable by BTT if there's a way to force that slight click and drag before the shortcut fires.