My first thought: what mining power does Iran have? Seems important.

It's worth remembering that the Iranians have as yet never claimed that the strait is mined. They have said that it may be. A lot of reporting misses this and assumes (perhaps deliberately) that the presence of mines is a fact.

But of course Iran doesn't need mines to enforce the blockade. They have drones and missiles that can be operated safely from 100's of kilometres away. They have anti-ship sea-skimming missiles. Not to mention the very large fleet of small armed fastboats.