I have no idea if they're currently building or not but I would imagine they were pretty close to completion before the lockdown. Of course it's just speculation but it is doing nobody any harm and just providing a bit of fun to pass the time.
Building was definitely continuing on site as of last week. As has been mentioned I posted before the names of species that were listed on the original plans before they were removed and replaced with the code names.
They have also previously said whilst they would never rule out holding any species there’s certainly NO plans to ever hold elephants due to the size of enclosures and the costs of upkeep.