This is rather a suggestion. I think that it's quite counter-intuitive that applying a Global Theme, which is under the "Appearance" module, could have effects that extend beyond what is configurable within that module. Task switcher is part of "Window Management", and (I can only assume here, based on my own preference) users typically want to set and forget the task switcher layout, but maybe change theme or colors or icons or cursors, from time to time. It makes sense then to group those items inside a Global Theme to enable them all with one action, but since the Task switcher is by your own admission something not related to Appeareance, I think that this one should not be affected. A way to work around this could be to consider it part of the Desktop layout (while it's technically not, I'd argue that it's got more in common with widget and panels, than with colors, icons and cursors...).
It depends on the Global Theme itself. Some have an opinion about which Task Switcher to use, some don't. IMO it's valid for themes to have an opinion about this, as it's possible and also valid for Global Themes to ship their own Task Switcher, and then of course they want to have you use it! However note that for Plasma 6, Breeze does not have an opinion about your Task Switcher, and does not change it. In addition, when applying a Global Theme, you have the option to make it not apply any of the things that it has an opinion about (such as the Task Switcher) if you don't want. I think that's good enough.