I thought about this a bit more. Lagrangian orbits are hellishly complex things that I don’t pretend to fully understand, but I think one can reach a conclusion from first principles.
Consider that any object in any orbit must be experiencing a centrifugal force pulling it away from the center of its orbit, and this must be balanced by an equivalent gravitational pull from the center. It cannot be any other way. This is further confirmed by looking at the gravitational potential contours posted previously. The halo orbit which is roughly perpendicular to the ecliptic takes the JWST both “in front” of L2 and behind it, where the gravitational potential is higher than at L2. This manifestly must be true throughout its orbit. And the farther it is from L2 along the earth’s orbital tangent (within some relatively short distance) the higher the gravitational potential energy and therefore the lower the kinetic energy (i.e.-speed). So I conclude that the normal rule for tangential velocity at apogee vs perigee applies.
Another way of looking at it is that the above supports the idea that a weight on a string, set moving so it describes an elliptical orbit, is a valid analogy. There is no mass at the center of its orbit, but it describes a Lagrangian type orbit due to the balance of forces between the string and the earth’s gravity. One observes that in a shallow ellipse, it moves much faster along the long side of the ellipse where it’s closest to its rest point (perigee) than the short side where it’s farthest (apogee). Indeed if the ellipse is squashed completely flat, you have a pendulum, which has zero motion perpendicular to its plane, and the velocity of the orbiting weight at apogee is precisely zero.
If I’m wrong about any of this I’d welcome any correction.