It is a well known fact that the groups composing the Taliban seek to obtain a Islamic emirate in compliance with Islamic laws; however, do they also seek to the foundation of a “Pashtunistan”, the same way Islamic Baloch separatists seek their ethnic land?
Not ... exactly.
Pashtun culture is traditionally very tribal. So it is much more natural for them to feel allegiance to their family groups, tribes, and clans. Effectively, this means they like their politics very decentralized. This is why the north western province of Pakistan bordering Afghanistan, which is also mostly Pashtun, has a reputation for being a "wild west" territory. Until recently, the Pakistan government found it best to let much of it operate entirely under tribal control.
Sure there's an affinity for other Pashtuns. Like most everyone else, Pashtuns feel that people from their own culture are more likely to have the right ideas about things. However, the main trans-tribal institution Pashtuns seem to respect is their religion (largely Sunni Muslim, of the Hanafi school, but also heavily influenced by their own culture). This is why they have a tendency to think in terms of establishing an Iran-style theocratic government when they really must have a super-tribal government at all, and if it has a role it is to enforce proper Muslim behavior.
Now one could argue that this is a kind of Nationalism, but only pushing the religious aspect of their identity. However, it is more properly termed something else. Essentially Islamist, but only for their culture's flavor of that faith. Their main concern seems to be that governments ruling over Pashtuns should be run according to Pashtun religious principles. Most of the rest of politics should be left to the tribes.
The political expression of these principles for the last few decades has been The Taliban.
The Taliban's ideology has been described as combining an "innovative" form of Sharia Islamic law based on Deobandi fundamentalism and militant Islamism, combined with Pashtun social and cultural norms known as Pashtunwali, as most Taliban are Pashtun tribesmen.
(Of course this is all gross generalization, which means it's trying to describe mass cultural behavior, not the feelings of individuals. No people are a monolith).
You have mentioned that "Until recently, Pakistan government... tribal control." Has there been a change in their mindset? Aug 24, 2021 at 17:58
1@WantARevolution - It was news to me too until I started researching this question, but it appears that in the last couple of years the "Federally-administered Tribal Areas" of Pakistan got rolled into a proper province under government control.– T.E.D.Aug 24, 2021 at 18:13
Thank you for your answer T.E.D. One thing that bothers me is why they try to achieve control over the Panjshir valley, which is mostly composed of ethnic Tajiks and Uzbeks. So if there is no ethnic consideration or national territorial one’s, why do the Taliban stop at these specific borders for their envisioned Emirate? Aug 28, 2021 at 21:46
I remarked that the Taliban have been trying to take over Panjshir Valley against the Northern Alliance. Which goes back to my point of what value they see against that territory, because if they are not fighting for a dual Islamic and ethnic cause, why just remain isolated to Afghanistan? Their support to and by people of Pashtun origin, and their disputes of the border with Pakistan makes me wonder this. This makes it seems Ethnic in nature but were that the case they have no reason to expand north. Aug 29, 2021 at 0:38
@Evamentality - Ah, I misunderstood. Well, the issue there is that the internationally-recognized borders of Afghanistan include that valley, not to mention it is very close to Kabul. That being said, they (Taliban) never took it before the US invasion, so its quite possible they'll be OK with just leaving it and the rest of the NE Takjik area alone for a while now as well. Particularly since they appear to have an ISIS problem in their own territory.– T.E.D.Aug 29, 2021 at 3:51