Must the state be paid for erections after benefiting from the market without the presence of its agents, and does this payment fall under the prohibited "tax on goods"?

If the commission is taken for the benefit of the market and the populace, in return for a service provided by the state, then there is no harm in imposing it to the extent of that benefit. It becomes a debt obligatory upon its owner, as mentioned by scholars, who cite the Prophet's (peace be upon him) command to return a third of Medina's fruits to the disbelievers, then half of them, and his command to dig the trench and place the wages of the laborers upon those who abstained. This ruling is known to be acted upon and to restrain one's tongue from criticizing the ruler, not for publicizing fault. However, if the state waives its claim for it regarding past sales, then it is not obligatory to pay it. But if the state takes it unjustly and without right, then it is not permissible for them to take it, nor is it obligatory to pay it.