How to check battery capacity of a new phone (iPhone SE)?
There's no way to check to see if the battery is genuine without opening it up and visually inspecting it.
When the battery gives you it's capacity, it's basing that on a moment-in-time measurement of the battery's charge against a known capacity value (1624 mAh for the iPhone SE; 1821 mAh for 2020 SE). Any 3rd party battery can have that capacity, but how they discharge is what makes the difference (quality of the cells).
That said, there are many reasons for quick discharge of your battery: an update to iOS may have a bug, apps being open or utilizing too much resources, etc.  For example, my own iPhone started exhibiting poor battery life the moment I upgraded to iOS 14.  I confirmed it by restoring a backup from iOS 13.
That said, &quot;way to short&quot; is very subjective - you need to define what way to short is in terms of hours of use compared to what Apple publishes.  However, it's been reported that battery life is a &quot;Major Letdown&quot; when compared to other manufacturers.  So, based on how you use the phone and the factors mentioned above, YMMV with respect to battery life.
If you're concerned that the battery may not be genuine, the only way is to physically open it and have an Apple technician inspect it.