So what's happening is Pakistan controlling afganistan?
In simple terms No.
You cannot control an entire country just like that.
In complex terms they don't control the country but rather have overwhelming influence over their domestic and international affairs as of now.
Contrary to the popular hopium being spewed here from the last few days Taliban is not some nachaniya who will start dancing for us if we throw some money on them. They are a ideological terror group which believes in the superiority of Islam and it's laws and follows the doctrine of Jihad to spread Islam around the globe.
After the fall of the first Afghan govt and the subsequent US drawdown the next generation of mujahedins were trained in a string of madrasas on the pak-afghan border by ISI to keep up the support at a time when US was reducing the aid and money inflow. Infact the indoctrination was so strong that these Jihad verses were included in the curriculum syllabus in Pakistan to nurture a strong sense of bonding back in 80s.
Most afghan leaders and their families hid in pakistan and many keep their families there till date. All these warlords like Ismail khan Aslam Farooqui Abu Bilal and sami ul huq who was also known as the "Father of taliban" had stayed in pakistan for years building their militia and hiding from their enemies some of then are pakistani nationals too. Every meeting at doha and the people who attended it was vetted by ISI.
Let us talk about "Mullah baradar" the person who is now designated to lead the new Afghanistan. He was captured by ISI in 2010 after immense pressure from the US due to his military expertise. He was on the hitlist of the US for a long time due to him launching multiple successful offenses against ANA.
Despite his capture ISI rejected all requests and attempts made by the US to get him or even talk to him to prevent a redux of sami ul huq who was killed by the US. After 9/11 both mulla umar and mullah baradar were hidden in pakistan to prevent their capture by CIA. The Doha peace deal was supposed to be signed by Sher Mohammad Abbas Stanikzai, but the ISI replaced him with Baradar as a signatory. Most importantly for pakistan it will be the lack of support and later on the clampdown on BLA and other organizations in Afghanistan that will help them shore up their borders.
What does all this mean for India?
Only time will tell. From 1996-2001 India taliban relation had remained frosty despite so called talks back then too. They had despite pressure kept all the hijackers under their safety during the NDA govt. Our strategic planners are not this dumb. If bribing taliban was possible we would have done that long back but the ideological difference is too vast and that prevents any sort of meaningful talks from taking place.