Vanadium is a Chromium-based browser (the same browser Chrome is based on), and these are the steps to setting Mojeek as the default search engine: [GrapheneOS] How to set Mojeek as the default search engine in Vanadium
It also explains a little of how it works:
Another glaring omission, though this is intentional because upstream Android Chromium doesn’t do this either, is the inability to add custom search engines. Vanadium needs to pick this up from the OpenSearch metadata; you can’t just add a new URL like in Firefox.
Chrome on Android will pick up this document when you make a search with mojeek.com: https://www.mojeek.com/opensearch.xml
This is the document which tells Chrome that Mojeek is a search engine and how to import it into “Recently Visited”.
I tried Chrome on Android last month, and I was able to set Mojeek as the default search engine. I’m not sure why you’re having difficulty, but I know Chrome also won’t pick up Wikipedia because it doesn’t serve an OpenSearch document.
This page is a little outdated because it doesn’t include the new OpenSearch method which was implemented in Chrome a year or two ago, but it explains another way of using Mojeek by default: Add Mojeek To your Chrome Android
I don’t think there is any way to convince Chrome to recognize Mojeek except through this method.
On the bright side, Google is looking into giving users the ability to add search engines manually this year: 1440189 - chromium - An open-source project to help move the web forward. - Monorail