There isn’t a web API option exposed for searching files across all backups currently.
The restore page relies on this REST method: duplicati/Backup.cs at master · duplicati/duplicati · GitHub
But it has some performance issues. Specifically it takes 3-5 seconds to look through the database for matches for one backup set, potentially growing much slower if modified to look at all id’s.
I think it would be best to bet on writing a new method, and SQL query, to support this use case. But to be honest I think the entire restore functionality could use a rewrite
Edit: I took some time out a few weeks back to go through that hole restore process and make some SQL queries to test what kind of performance I could get. I have the notes on it, including queries, but I didn’t get around to clean it up and posting it on the forum. Maybe those queries would be interesting if someone is looking into this feature?