Who (consumer or producers) ultimately shoulders the burden of a tax (in this case, a carbon tax to internalize the externalities I referred to) depends on the

Who (consumer or producers) ultimately shoulders the burden of a tax (in this case, a carbon tax to internalize the externalities I referred to) depends on the price elasticity of demand. If consumers are relatively price inelastic, then they'll shoulder the cost of the tax. If consumers are relatively price elastic (sensitive), then they (at the margins) switch to alternatives and then the producers ultimately pay via lower volumes and tighter profit margins. I think we are seeing what happens when oil increases significantly for a prolonged period - emergence of EVs, switch to heat pumps, etc. etc.