If you already have Opus 13, it may be worth trying it first, as that could solve the issue by itself. We can now run a lot of context menus in a separate process, isolated from the rest of Opus, which sometimes helps with compatibility (as well as protecting our main process from shell extensions that crash).
For what it's worth, I've been using dBPowerAmp for a long time without issues, although I am still using quite an old version.
That said, if you want to stay on 12, or if you install 13 and see the same issue, we might be able to work out what's going on via some process snapshots.
Here are the instructions for making them: Manually generating process snapshots
Before making them, run the menu item a few times in a row. Until it's in a state like the one you described (new windows haven't appeared but seem to be building up). Then make a few snapshots via the method I linked to.
With those we might be able to see if there are a bunch of threads stuck waiting for something to happen, or similar. Although it will depend a lot on what's causing the delay and how the menu extension is implemented.