Whenever we have massless degrees of freedom, there is usually some underlying reason. For massless scalar fields, Goldstone’s theorem typically provides the reason. But we can also invoke Goldstone’s theorem to explain why the photon is gapless: we just need to extend its validity to higher form symmetries.
In Maxwell theory, there are two 2-forms which are conserved. Each can be thought of as the current for a global 1-form symmetry: $$ \text{Electric 1-form symmetry}: J_e \propto *F $$ $$ \text{Magnetic 1-form symmetry}: J_m \propto F $$ The electric 1-form symmetry shifts the gauge field by a flat connection: $A → A+d\alpha$. In contrast, the action of the magnetic 1-form symmetry is difficult to see in the electric description; instead, it shifts the magnetic gauge field $\tilde{A}$ by a flat connection. Relatedly, the electric 1-form symmetry acts on Wilson lines $W$; the magnetic 1-form symmetry acts on ’t Hooft lines $T$.
In the Coulomb phase we have $\langle W\rangle \neq 0$ and $\langle T\rangle \neq 0$, so that both symmetries are spontaneously broken. But a broken global symmetry should give rise to an associated massless Goldstone boson. This is nothing but the photon itself.
See section 3.6.2 in David Tong: Lectures on Gauge Theory.
I will be glad to discuss it:)