I am suggesting you create a route to get open source applications that can't afford $99 to spend on a apple developer license to work with 1password's connect to browser functionality. I am intentionally trying to leave have how you do that open.
1password in the browser is a pretty terrible experience without the connection to the app.
How most of these work is just PK encryption, and the authority maintains a CA in that case, however that was just an example. Another approach might be that people making open source browsers just submit a hash to you of the build and you check that the binary matches that has before running it, obviously as a technical approach that's a lot more of a pain than using PK encryption. There are lots of options here, and I as someone external to your company can't really recommend which would work for you. This is not a novel and interesting problem, it is well solved.
I want to point out that you do not have to use Apples notarization process to authenticate browsers, you could have chosen a method that does not disadvantage those who are less well off. They didn't make you do this, unless there is something going on here that I have missed.
