That is not correct.
>...Smith's first maxim of taxation, from Wealth of Nations, is that the "subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state."
>Taxation in proportion to revenue is not progressive taxation. It is proportional taxation—in modern terminology, a flat tax.
https://reason.com/2023/06/04/adam-smith-wasnt-a-progressive...
In terms of Mill, I think he advocated for inheritance taxes, but in terms of "steeply progressive taxes" he wrote:
>...To tax the larger incomes at a higher percentage than the smaller is to lay a tax on industry and economy; to impose a penalty on people for having worked harder and saved more than their neighbours.
https://oll.libertyfund.org/titles/mill-principles-of-politi...