TL;DR: We could probably conclude that all countries that oppose the US and/or India are quite welcoming of the Taliban i.e Pakistan, Russia, and China. Some of the Gulf countries have said they support stability in the region and have claimed they support the desire of the people of Afghanistan, so they might throw their weight around after it's a bit clear on how the Taliban is acting.
The Taliban are attempting to find allies as per this source:
But in recent weeks, top Taliban leaders have been on a whirlwind international tour, visiting Iran, Russia, and China.
China is planning on recognizing the Taliban as per this source:
China is prepared to recognize the Taliban as the legitimate ruler of Afghanistan if the terrorist group manages to overpower the democratically elected government in Kabul, US News has learned.
For which, one of the main reasons might be because China has been interested in the natural resources of Afghanistan evidenced by its previous interaction with President Ashraf Ghani's government :
China has reportedly promised big investments in energy and infrastructure projects, including the building of a road network in Afghanistan, and is also eyeing the country's vast, untapped, rare-earth mineral deposits.
Russia seems to be playing a game of wait-and-watch although it's to be noted that they have been trying to establish ties with the Taliban for a significant period of time as per this source:
Kabulov said on Monday that Moscow's long campaign to build ties with the Taliban appeared now to be paying off. "It's not for nothing that we've been establishing contacts with the Taliban movement for the last seven years. We saw that this force would in the end if not completely come to power would play a leading role in the future of Afghanistan in any case," Kabulov told Ekho Moskvy.
Kabulov said Russia would decide on recognising the new Taliban government based "on the conduct of the new authorities" and that his country "established working contacts with representatives of the new authorities".
Iran has welcomed the defeat of the US and has claimed it wants peace amongst all the groups in Afghanistan. Iran has claimed it supports any efforts to bring stability to the region but hasn't been clear on whether it believes the Taliban to be such a force as per this source:
"America's military defeat and its withdrawal must become an opportunity to restore life, security and durable peace in Afghanistan," Iran's state TV quoted Raisi as saying.
"Iran backs efforts to restore stability in Afghanistan and, as a neighbouring and brother nation, Iran invites all groups in Afghanistan to reach a national agreement."
Saudi Arabia has voiced out its support for stability and has advocated that it supports any choice that the people of Afghanistan desire as per this source:
A statement issued by the Saudi foreign ministry on Twitter added that the kingdom "stands with the choices that the Afghan people make without any interference," expressing hope that the situation in the central Asian state stabilises as soon as possible.
Qatar is supporting a peaceful transition of power but isn't very clear on its support of the Taliban as per this source:
Fellow Gulf state Qatar said it was seeking a peaceful transition in Afghanistan and was doing its utmost to help efforts to evacuate diplomats and foreign staff in international organizations from the country.
Bahrain has said that it will decide on what to do after consulting with the rest of the GCC as per this source:
"The council of ministers has tasked the foreign minister to coordinate and consult with the GCC states regarding the developments in Afghanistan, in the framework of Bahraini presidency" of the group which also includes Saudi Arabia, the United Arab Emirates, Qatar and Oman, it said on Twitter.
