quantum field theory - Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

I suppose there was a discussion already on speed-of-gravity-and-speed-of-light.

But I silly wonder whether all the massless mediators of four fundamental forces, i.e.

Graviton: $g_{\mu\nu}$ (gravity)

Photon $\gamma$: $A_\mu$ (electromagnetism)

Gluons: $A_\mu^a$ (strong interactions)

Necessarily travel at the same speed? Is there a no-go theorem or theoretical proof to say that it is impossible to have these three mediators have different speeds?

Or does QCD confinement makes the story of gluons any different from gravitons and photons?

[ps. excluded massive $Z^{0}$ and $W^{\pm}$ bosons (weak interactions)]

Another way to say this: Speed of photon, graviton, gluon all equal to $c$? or Whether all massless particles necessarily have the same speed?

Note add: Notice however, in condensed matter systems, there can be emergent gauge fields and emergent massless particles (Dirac or Weyl cones), but their speeds need not be the same, unless there is some emergent symmetry...