It can't be done gracefully with a client. Since there is no way to apply multiple tags at the API level, in order to get the job done, you need to resort to throwing away the data you don't want after the query response comes back. Instead of, well, just not pulling it down in the first place.
Not worth it in my opinion, especially considering the itch developers may decide to implement the API level filter in the future.
But of course it's gardenapples application.
I think removing tags from search results is a reasonable work around (I have zero programming knowledge btw so not sure if that's what you mean).
Anyway if the feature is too awkward or difficult to add I understand. I'm not sure about the dev's given how many years it's been requested. I think I'll keep my expectations low and/or think of something by myself.