AviK
The fact that the free dictionary states that the land used as a military base is considered a form of territory doesn’t make it sovereign soil. In most cases it is leased for exclusive use by the military and the lessor has agreed that the lessee may govern what goes on withing the leased premises. This is quite different from sovereign soil.
In your reading of the section of Article 22 regarding entry by the host country: In many cases the US leases the embassy premises. The land is not owned by the US and cannot be US sovereign soil. Many countries do not allow foreigner to hold title to land in their own names.
The important point is that military bases, embassies and consulates are not sovereign US soil although they have special rights.