The Wikipedia page is wrong, or at least not totally right. Hong Rengan's 1859 manifesto, the New Treatise on Aids in Administration 資政新篇, says the following:

興車馬之利，以利便輕捷為妙。倘有能造如外邦火輪車，一日夜能行七八千里者，准自專其利，限滿准他人仿做。若彼願公於世，亦稟准遵行，免生別弊。先於二十一省通二十一條大路，以為全國之脈格，通則國家無病焉。

Promote the use of vehicles and horses, [that are] as convenient and as fast as possible. If there are those who can create locomotives like [those in] foreign countries, which can traverse seven or eight thousand li (3.5-4km) in a single day and night, will be granted a patent, once it has expired others may emulate them. If they are willing to make the invention public, they should also seek [official] approval and act accordingly, so as to avoid confusion. First, in the twenty-one provinces, build twenty-one great roads, as though veins across the whole country, freeing it from illness.

So pedantically speaking, while Hong promoted the construction of railways and the establishment of transport links across all 21 provinces, he was not proposing the construction of railroads across 21 provinces. As for which 21 provinces, the Qing technically included the three Manchurian divisions of Jilin (Girin), Fengtian (Abkai-imiyangga) and Heilongjiang (Sahaliyan-ula) alongside the 18 traditional Han Chinese provinces to form 21. However in theory the administration of the three Manchu provinces was exclusively a preserve of Manchu officials, with separate officials responsible for Han affairs. Over time this had morphed into parallel hierarchies of Manchu and Han officials in the so-called 'Three Northeastern Provinces'. Hong Rengan evidently was including these three provinces in his postwar vision. Unfortunately, the Taiping's actual long-term plans for the Manchu empire have been woefully understudied, and so I can't say how much Hong Rengan was diverging from prior Taiping schemes here.

Sources, Notes and References

• Franz Michael and Chung-li Chang's The Taiping Rebellion: Documents and Comments contains a translation of Hong Rengan's 資政新篇.
• A digitised version of the Chinese text can be found at the Chinese Text Project.