The transaction associated with this command is not the connection's active transaction

The fix is fairly simple: if you want a Dapper query to participate in a connection, explicitly denote that intent:

private async Task<EResult> ProcessDepotAfterDownload(ManifestJob request, DepotManifest depotManifest)

{

    using (var db = await Database.GetConnectionAsync())

    using (var transaction = await db.BeginTransactionAsync())

    {

        // add `transaction` to method call below

        var result = await ProcessDepotAfterDownload(db, transaction, request, depotManifest);

        await transaction.CommitAsync();

        return result;

    }

}

private async Task<EResult> ProcessDepotAfterDownload(IDbConnection db, IDbTransaction transaction, ManifestJob request, DepotManifest depotManifest)

{

    // pass `transaction` to Dapper's QueryAsync below

    var filesOld = (await db.QueryAsync<DepotFile>("SELECT `ID`, `File`, `Hash`, `Size`, `Flags` FROM `DepotsFiles` WHERE `DepotID` = @DepotID", new { request.DepotID }, transaction: transaction)).ToDictionary(x => x.File, x => x);

    ....

}