Studies that associate Durani Kingdom with Afghanistan scarcely acknowledge the fact that “Afghanistan” was rarely used as a geographic term in sources predating 19th century. This includes chronicles produced under the auspices of various Timurid, Mughal, Safavid and post-Safavid rulers who exercised authority over the territories comprising what is today Afghanistan in the pre-Durani era. The same is true for documents produced at the court of Aḥmad Shah, which are noteworthy for not containing any references to “Afghanistan” despite the fact that the Abdali is widely regarded as the country’s “founding father". On the other hand, geographic terms like Turkistan, Khurasan and Hindistan are regularly encountered in sources produced in that period.
In his titles he doesn't call himself 'King of Afghanistan'. In his biography, nowhere he calls himself Afghan. If you have any source that disputes this i would love to know. The reluctance has roots in the word 'Afghan' being an exonym not something Pashtuns chose for themselves initially.
Ahmed Shahs paternal sadozai relatives lived in Multan from before. Infact presence of pakhtuns in Multan and its vicinity was way before pre islamic era due to its proximity to Takht-e-Sulaiman ,a traditional pashtun legend. This has been stated by Al Beruni in his book. Even Herdotus (500 BC) mentions boundaries of the partylike land extend up to eastern province of Arachosia ( river chenab ).
Its important to mention not only did Ahmad Shah grow up in Multan, he married there and had children there. He spoke local language and had locals in his army. So much so Multan also didn't get raided by Nader shah for the same reasons. His children who later inherited the kingdom died in present day Pakistan. Abdali himself died in Toba Achakzai near Chaman (Pakistan) and got burial in Kandahar(Afganistan). Abdali clan origin Arghistan is in Afghanistan right next to Pak-Afghan border apart from the fact that Abdali had his HQ in present day Afganistan therefore Afghans have right to Abdali as much as Pakistanis do.