[edit: typo, I use "ast" not "ask"]
Great thread, thanks. As for the issue of typing ease, you could consider using Autohotkey for asterisk and other punctuation. I have a simple method similar to the hotstring method, so I type "ask" instead of hitting an asterisk key. I don't even have an asterisk key, because I use a 34 key Ferris ZMK/QMK keyboard. So then it becomes super easy to type asterisk, which is a useful symbol in general, and the point applies to other non-alphanumeric symbols. Even with a standard zillion key keyboard, I can type a few letters faster than reaching for some key way off the homerow.
Another approach with Autohotkey would be to create an intermediary stage of your filter bar input that allows you to type the natural strings as in Everything, TotalCMD, etc and then they are automatically converted into the DOpus strings with asterisks or whatever. So instead of typing directly into the DOpus filter bar, you could have some trigger/command like, say "fil", that sends the string to Autohotkey to be converted and sent to the DOpus filter bar. So then in your mind you are always typing search strings in the same unified interface format of {space}=AND and the only difference is which app context you are in, which is resolved before you start typing the string. Otherwise it would probably cause a lot of extra cognitive processing if you have to context-switch and format-switch in the middle of typing the search string.
To give another flavor of this type of Autohotkey integration, the way I currently use the DOpus filter bar is by setting the DOpus filter bar activation keyboard shortcut to an arbitrary obscure Unicode symbol that I'd otherwise never use (e.g. ䷂, a yijing hexagram) and then via Autohotkey when I type "fil" that symbol is sent.