Bromite author here ( https://www.bromite.org ); I was contacted some time ago about the possibility to maintain a modified version of Bromite with a customised /e/ home page and list of search engines. Nothing particularly murky there, but after some Q/A I did not want to proceed with this type of cross-branding because fundamentally I do not want Bromite to be using or be affiliated with any cloud service and I con…
The AUTHORS file also mentions being a fork of Bromite, but doesn't list any authors that aren't part of the project: https://gitlab.e.foundation/e/apps/browser/blob/master/AUTHO...
It looks like your patches have been changed to renamed Bromite to Browser in user-facing code though. Have you already asked them to add a reference to Bromite somewhere in the about screen? Maybe create a pull request to make it easier for them to accept your request if the devs themselves are lazy. They obviously won't rename the browser shortcut, but adding a reference in the "About browser" section shouldn't be too much to ask for.
Unrelated: I understand your position on cloud providers, but I think /e/ is different from MS or Google in that it's possible to swap out most of the integrations with your own servers (it's all a bunch of glued-together open source services, after all).
Without cloud integration, I doubt /e/ would reach any sort of mainstream of non-technical cult status at all. You'd be left with an app store on top of a build of LineageOS. It's the services delivered with the system that a) distinguish the project from LineageOS without GApps and b) provide basic usability many normal users would miss otherwise.