Only administrator level users can approve timesheets. Since Intervals features project level permissions, managers only see projects where they share access with a resource so they could potentially only have a partial view into what the person has worked on.
Administrator level users see all projects and are not limited by the project permissions, so any administrator level user can approve time. One workaround that some Intervals users that need this flow have done is running reports then approving time. They have a report by a manager then approve as an administrator workflow in place for the approval process.
If that flow might work for you the summary report is probably the best report since the output looks very similar to timesheets.