Photons have an energy vector called the Poynting vector, gravity defines energy gradients based on direction from masses, electric fields are always defined with vectors, there's the electromagnetic four-potential, the vector potential that gives rise to magnetism, etc...

Pyonting vector is the direction of a energy flux (in units W/m2). the other fields explain how energy changes in 3D space (since they exert a force, and so moving in space with a force applied takes or gives energy).

Energy is measured in Joules, so if the thing is measured in some other unit that does not have some sort of direct tie back to Joules then it is something other than energy.

It might seam sensible that a moving object with a velocity along some vector also has an kinetic energy pointing in the same vector. But if you take something like a tuning fork that oscillates with both of its prongs moving opposite of each other and sum the kinetic energy of both prongs as vectors you get a total kinetic energy in the fork as 0. Even tho there clearly is energy there and it can be used to move other things such as air to create sound. Energy often appears in math along side of vectors quantities (ie velocity and force) but that doesn't automatically make it a vector too (for example dot product operation used in kinetic energy produces a scalar result)

And before you bring it up, yes energy can appear as a vector in quantum mechanics. It is used to make the weird quantum mechanics math work (Much like complex numbers are also used to make some of our other math work)