I don't totally understand the details of what you need, but here's some info.  If you rotate a selected model using the "Rotate model" mouse mode then its position matrix changes.  First Python to get the list of selected models is

session.selection.models()

If it is a volume (ie map) model that got rotated then I could find the selected volumes like this

from chimerax.map import Volume

volumes = [v for v in session.selection.models() if isinstance(v, Volume)]

And if I wanted to print their 3x4 position matrices (first 3 columns are the rotation, 4th column is a translation done after rotation)

for v in volumes:

    print (v.position.matrix)

Now I don't know what you mean by "update the rotation angles".  Are you trying to record Euler angles?  If so you could get the Euler angles in z-x-z convention like this

from chimerax.geometry.matrix import euler_angles

for v in volumes:

  alpha, beta, gamma = euler_angles(v.position.matrix)  # Angles in degrees

  print ('Volume %s Euler angles %.2f %.2f %.2f degrees (z-x-z convention)' % (v.name_with_id(), alpha, beta, gamma)

In Chimera the openModels object holds the list of models.  In ChimeraX this is session.models.  For example to show the names of all models:

for m in session.models.list():

  print ('#' + m.id_string + ' ' + m.name)

The programmer documentation

has info about the various ChimeraX functions, for instance for models

https://www.cgl.ucsf.edu/chimerax/docs/devel/core/models.html