How to calculate 3D distance (including altitude) between two points in GeoDjango

Prologue:

This is a question arising often in SO:

• 3d distance calculations with GeoDjango
• Calculating distance between two points using latitude longitude and altitude (elevation)
• Distance between two 3D point in geodjango (postgis)

I wanted to compose an example on SO Documentation but the geodjango chapter never took off and since the Documentation got shut down on August 8, 2017, I will follow the suggestion of this widely upvoted and discussed meta answer and write my example as a self-answered post.

Of course, I would be more than happy to see any different approach as well!!

Question:

Assume the model:

class MyModel(models.Model):
    name = models.CharField()
    coordinates = models.PointField()

Where I store the point in the coordinate variable as a lan, lng, alt point:

MyModel.objects.create(
    name='point_name', 
    coordinates='SRID=3857;POINT Z (100.00 10.00 150)')

I am trying to calculate the 3D distance between two such points:

p1 = MyModel.objects.get(name='point_1').coordinates
p2 = MyModel.objects.get(name='point_2').coordinates

d = Distance(m=p1.distance(p2))

Now d=X in meters.

If I change only the altitude of one of the points in question:

For example:

p1.coordinates = 'SRID=3857;POINT Z (100.00 10.00 200)'

from 150 previously, the calculation:

d = Distance(m=p1.distance(p2))

returns d=X again, like the elevation is ignored.
How can I calculate the 3D distance between my points?