The only thing that could be wrong there is the order in this part:
$count = $query->count();
$formatted_date = $date->format('Y-m-d H:i:s');
$query->where('measurements.created_at','>=',$formatted_date);
for the where statement is applied after the count is fired, so your $count holds value ignoring that where. Just swap the two and it may get you the result you need.
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