An aircraft in a 45 degree banked turn has a horizontal lift force
vector equal to the weight of the aircraft. Although the Coefficient
of Drag is much larger for the aircraft profile, it seems there must
be a significant side drag force on the aircraft as a result of the
lateral velocity created.
A sideways force component does not imply a sideways velocity component. That is an Aristotelian way of thinking. Nowadays, we understand that a force component drives an acceleration component, not a velocity component. And turning flight is a form of acceleration, even though the magnitude of the total velocity vector may remain constant. The aircraft is constantly accelerating toward the center of the turn. But this does not imply that there is any velocity component towards the center of the turn.
How to calculate lateral velocity of a turning aircraft
In a "coordinated" turn1, the lateral velocity toward the center of the turn, in the airmass reference frame, is always zero, because the aircraft is always pointing in the same direction as it is moving through the air.2
The critique of the actual formulae presented in the question, will be left to other answers.
It's important to note that turns tend not to be completely coordinated unless the pilot (or the autopilot) is making a rudder input to accomplish this. An aircraft has some tendency to sideslip-- the nose tends to point slightly toward the "outside" or "high side" of the turn. This tendency is typically most pronounced as an aircraft is entering the turn, but is typically present to some degree even in a constant-banked, steady-state turn, especially at lower airspeeds, or more precisely, at lower "scale speed", which is inversely related to the time to cover one fuselage-length. The reasons for this involve the difference in airspeed (and therefore drag) between the inboard and outboard wingtip, the effect of the curving flight path and relative wind on the vertical fin, etc, and are best addressed in detail elsewhere, but this effect does have a very significant effect on lateral stability. It is the reason that geometries like dihedral, sweep, and the multiple different effects related to high-wing or low-wing geometry, do affect an aircraft's lateral stability, including an aircraft's rolling-in or rolling-out tendencies in a stabilized constant-banked turn, in a situation where the pilot is making roll inputs as needed with the ailerons, but is not using the rudder to ensure that the turn is completely coordinated. Calculating this sideslip angle in any given situation is far beyond the scope of this answer!
It's pretty obvious that the question was intended to be about velocities in the airmass reference frame, or in no-wind situations. Computing the lateral component of the groundspeed at any given instant is a solvable problem, but best addressed elsewhere.