Hello!
Anyone using Stage Manager out there? 
Before Sonoma, you were able to Shift Click a window to add it to your Set and then Shift Click to remove it. But Apple seems to have removed that ability to quickly remove a window from a Set... so I made an action to add it back! 
But instead of using Shift Clicking and messing up the default behavior, I changed the shortcut to CMD + Shift Click - also the window doesn't need to be in focus - since BTT will make it the mouse under the cursor the focused window before removing it. Sweet.
If you enjoy this preset, please check out some of my other projects or consider donating. Thanks for checking out my preset! 
-Josh
Here is what it looks like:
Installation
StageMangerShiftClick_v1.bttpreset (3.2 KB)
Or just copy and paste the following under Normal Mouse:
[
{
"BTTLastUpdatedAt" : 1709330108.694175,
"BTTTriggerType" : 1000,
"BTTTriggerTypeDescription" : "Leftclick (needs modifier key)",
"BTTTriggerClass" : "BTTTriggerTypeNormalMouse",
"BTTUUID" : "7D6A21F6-4277-4047-931B-1207D54C3DDD",
"BTTPredefinedActionType" : 366,
"BTTPredefinedActionName" : "Empty Placeholder",
"BTTEnabled" : 1,
"BTTEnabled2" : 1,
"BTTRequiredModifierKeys" : 1179648,
"BTTOrder" : 6,
"BTTAdditionalActions" : [
{
"BTTLastUpdatedAt" : 1709330108.69449,
"BTTTriggerType" : -1,
"BTTTriggerParentUUID" : "7D6A21F6-4277-4047-931B-1207D54C3DDD",
"BTTIsPureAction" : true,
"BTTTriggerClass" : "BTTTriggerTypeNormalMouse",
"BTTUUID" : "014E15E5-C0E5-4D2C-B7E6-EB7664AE0DCC",
"BTTPredefinedActionType" : 204,
"BTTPredefinedActionName" : "Activate\/Bring to Front Window Under Cursor",
"BTTEnabled" : 1,
"BTTEnabled2" : 1,
"BTTOrder" : 0
},
{
"BTTLastUpdatedAt" : 1709330108.6947122,
"BTTTriggerType" : -1,
"BTTTriggerParentUUID" : "7D6A21F6-4277-4047-931B-1207D54C3DDD",
"BTTIsPureAction" : true,
"BTTTriggerClass" : "BTTTriggerTypeNormalMouse",
"BTTUUID" : "74B7D6A2-900B-4AE7-B29C-12EE1EB9E277",
"BTTPredefinedActionType" : 345,
"BTTPredefinedActionName" : "Delay Next Action (async \/ not blocking)",
"BTTDelayNextActionBy" : "0",
"BTTEnabled" : 1,
"BTTEnabled2" : 1,
"BTTOrder" : 1
},
{
"BTTLastUpdatedAt" : 1709330108.6949151,
"BTTTriggerType" : -1,
"BTTTriggerParentUUID" : "7D6A21F6-4277-4047-931B-1207D54C3DDD",
"BTTIsPureAction" : true,
"BTTTriggerClass" : "BTTTriggerTypeNormalMouse",
"BTTUUID" : "0CAFFF3E-A3E3-4A77-ABA8-D3C557AD2859",
"BTTPredefinedActionType" : 124,
"BTTPredefinedActionName" : "Trigger Menu Bar Menu-Item",
"BTTMenubarPath" : "Window;Remove Window from Set",
"BTTEnabled" : 1,
"BTTEnabled2" : 1,
"BTTOrder" : 2
}
],
"BTTGestureNotes" : "Quickly remove windows from a Stage Manager’s Set"
}
]