I agree I would generally prefer clients to be idiomatic for the target language but in the case of LINQ providers I understand not doing them since they are quite involved to implement.

You can probably leverage something like https://linq2db.github.io/ and replace some parts of their SQLite provider with HTTP calls to avoid coding most complicated parts. This would be for the raw sql API, for the records API I'm not sure LINQ makes sense since from what I saw in the docs it would be a pretty small subset of LINQ anyway. An easy way to generate the model classes from the DB schema would be nice too (a source generator accessing the schema via some endpoint?).

Edit: it's nice seeing C# getting some love early in a project, I'm used to fallback to js/ts to try the new stuff :)