How likely are we to see an extended 052D or a 054E with additional 16 VLS?
That would make it basically a Burke equivalent
Quite unlikely. Both are aging platforms. Those stealthy lines might belie the fact that their hull foundation goes back to 30 years for the 052X, going back to the first pair of 052 Harbin and Qingdao, and the 054X goes to back about 20 years now from the first pair of Maanshan and Wenzhou. The simplest way to get more VLS is to mass produce 055s. This might sound big, complex and expensive but that sounds like the first Type 052C when it was first built, people are saying China won't build any more than two or four of these. Well, they did build six eventually and 25 of its immediate successor.
As time goes on, China's GDP rises, and you have the warship inflation trends, the 055 won't seem as big or as expensive or as unique in the future. As more units ar built, its cost per unit is also expected to go down.
Now with frigates, if you want more VLS, you build more frigates.