Only when TOS Enterprise
is actively maneuvering or turning, or getting knocked around in a storm, do I recall seeing her point in a different direction.
Unless I'm forgetting something, once she's settled on course, she's always going forwards or backwards.
And she goes backwards only in an emergency. I've never seen the Enterprise
warping through space facing sideways.
(But let's not try to get into relative to which frame of reference the direction of velocity is specified with respect to. Star Trek
physics at impulse power is well-known to violate Newtonian physics as is. As far as I'm concerned, the direction she's facing and the direction she's moving is what they both appear
to be on screen.)