If the collection has a large number of tags (e.g. AnKing v11 deck), the display of the list of matching tags when using the Add Tags... or Remove Tags... options in the browser is slow. It takes >1 second for the first letter to appear in the search box. The performance improves as more letters are entered, which is probably because the number of matching tags decreases.

However, an addon (Better Search) can display the list of matching tags almost instantaneously when searching in the main search box of the browser.

So, I believe that the code for getting the list of matching tags in Anki needs optimization.

Edit:
The display of tags is fast in the Add note window also. So, I guess that the Add Tags... and Remove Tags... options use an older and less efficient function while the Add note window uses a newer and more efficient function.