As a DuckDuckGo fan as well, I'd have loved to see them/DuckDuckGo develop their browser on the top of Firefox with Mullvad as a partner with deep integrations.
They are. Mullvad browser seems to be aimed at users that want a hardened Firefox out of the box with additional Mullvad extensions, while Firefox with Mullvad installed manually is all manual setup.
We did not, we made a front end to the Google Search API.
Our search engine performs the searches on behalf of our users. This means that rather than using Google Search directly, our Leta server makes the requests.
I thought it'd be possible by simply turning off "Always use private browsing mode" setting, but it doesn't seem to work. Sessions are still cleared upon browser exit.
In my case, I had to turn off that setting because without it, 1Password wouldn't work.
Both Chrome and Firefox are working on native iOS versions in preperation for the expected opening up of iOS this year so would imagine they can just fork that and release their version.
https://archive.ph/WLKRs