The first time I open a link inspector using "[[", Ctrl-K, or the toolbar button, it takes about 5 seconds on my laptop. The subsequent times I do it in the same editing session it opens immediately.
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(This may be a dupe. I remember reporting it a few weeks ago, but I cannot find it now.)
This also happens for me when using Opera 12 (which is somewhat slow compared to more modern browsers). The inspector dialogs are still using isolation (rendered inside an <iframe>) and I can reproduce using isolated dialogs in the demo, so that's probably the reason. We're apparently working on killing isolation, though.
I also vaguely recall this having been reported already, but can't find it. I only found T72467, which was actually an entirely separate issue.
I'm not sure what happened, but I cannot reproduce it on Firefox in the version that is currently deployed in Wikipedia. The link inspector appears immediately.
What happened is that inspector dialogs no longer use isolation, so my
guess was probably correct.