Proposal:
Add properties angle and angle_rad to pygame.Vector2 with getter and possibly a setter.

vec.angle_rad == math.atan2(vec.y, vec.x) == vec.as_polar()[1]  # note: no vec.angle_rad_to() method
vec.angle == -vec.angle_to([1, 0]) == degrees(vec.angle_rad)

(These angles are normalized: degrees within interval (-180, 180], even if set to an angle outside this range.)
The zero vector has an angle of 0.

Reasons:
In math, the angle of a vector is often relative to the positive x-axis (increasing angle from 0 goes towards positive y-axis).
For example, polar coordinates and trigonometry functions are connected to vectors through their angle to positive x-axis.
vec == Vector2(r * cos(theta), r * sin(theta))

The current ways to get these angles are indirect and less readable, for such an (IMO) important aspect of vectors. See above. In as_polar() result, the length is available via vec.length, but the angle is not directly available.

In a codebase, it's convenient to only have to store one float (angle to +x axis) to mark the direction of something, rather than another vector (especially when the distance between two points is unnecessary/inapplicable). Many physics libraries or engines use angles like this heavily, usually using radians. Even if angles are technically only relative, to store them conveniently there has to be 'absolute' angles.

# Before
self.angle = (vec2 - vec1).angle_to([1, 0])
# After
self.angle = (vec2 - vec1).angle

# Before
self.angle_rad = math.radians(vec1.angle_to(vec2))
self.angle_rad = vec2.as_polar()[1] - vec1.as_polar()[1]
# After
self.angle_rad = vec2.angle_rad - vec1.angle_rad

# Before
vec.rotate_ip(angle - vec.angle_to([1, 0]))
# After
vec.angle = angle