Just a quick note for future requests: I know it feels weird, but creating many separate topics makes it much easier for me to handle. Such long lists are hard for me to prioritize or link them with existing requests. Often times I have a few minutes to look at something and short requests allow me focus on that and fix/add it.
Also often feature requests or bugs stay open for longer times because I had to prioritize other stuff, finding them again is much easier if the title clearly describes the content.
Also other users of the forum who would be able to help for some of the points might never find it because of the generic title.
Just a few quick comments, I'll add more for your points later today!
1.) An option to enable/disable a scroll blocking mode is high on my TODO list as it has been requested many times 
Should be added very soon.
However for gestures: have you tried to just create a set of BTT trackpad/magic mouse gestures that are only active for your webview?
2.) Good idea.
3.) Mission Control & App Expose are essentially black boxes, but there is one advanced condition property that you can use. It's called: missioncontrol_active and will be 1 if mission control or app expose are active
4.) See Disable/hide unneeded BTT sections - Feature Requests - BetterTouchTool Community (folivora.ai)
5.) Sorting is currently not possible because in most sections the order of the items has not only a visual but also functional meaning. However I agree that it would be helpful, just not sure how to implement without potentially breaking stuff.
6.) Good idea
7.) Already added for Ventura (In general the ventura window switcher is completely different than the old one with tons of new functionality, the old one will unfortunately not be developed further) . I highly recommend to upgrade to Ventura as BTT will make use of lots of the new SwiftUI features in the near future
8.) See 7
9.) Unfortunately every app can style and implement toolbars however they like, thus a universal way to recognize that is hard and might never cover all cases. Maybe I can add a variable that covers most common cases, so you just need to add additional specific conditions you need.
10.) Can you elaborate? I think you can already do that with the custom move / resize action, but probably I'm missing osmething.
11.) Logitech has their own (mostly undocumented) device protocol, but I'm currently working on fully supporting all features of all Logitech mice via GitHub - libratbag/libratbag: A DBus daemon to configure input devices, mainly high-end and gaming mice This is a massive feature , but the next BTT alpha will already have a way to recognize your buttons via a new feature called "Generic Devices"
Currently the easiest way is to assign a keyboard shortcut via the logitech software, then catch that shortcut in BTT.
Problems:
1.) macOS needs to compile the text you enter for Apple Scripts before running them. BTT caches the compiled versions, but if for some reason the BTT Apple Script runner crashes or you restart BTT, the compiled versions will be gone. You could get around this by creating a compiled scpt file via Apple Script Editor and calling this from BTT, they might be slightly faster.
2.) There might have been some improvements with the latest alpha for this (or maybe with the version I'm currently running locally - I'm not sure if I have already released this).
There might be more work necessary
3.) This might be because the system somehow catches a right click before BTT can recognize the three finger tap. You could try to add a right click with the dock condition in the "normal mouse" section in BTT
4.) Weird, I'll look into this.
5.) It's a system limitation, but I could workaround it by first activating the window, then closing it.
6.) I'll look into this