For your request, I feel like we would most likely default to having customers looking to make searches like that use the HTTP Request card or the three step method you outlined. I think the added functionality is great, but the added fields and options make the card that much more difficult to use. It would require a decent amount of work to figure out how to make the huge number of options available in the fields section not be overwhelming.
The formatting for the Filter, especially if you’re only filtering on something like projectID, would be as simple as “projectID=INSERTIDHERE”.
To elaborate, the formatting that David posted above for the API query URL is actually the formatting you’d be looking to use in this Filter field. Specifically, the part after the question mark and before the “fields” section (because that part is handled by Azuqua).
So if you were to take the URL query above and filter it down for an event it would look like this: