If something becomes a copy of Protean Thaumaturge, it also has the constellation ability.

A constellation ability triggers whenever an enchantment enters the battlefield under your control for any reason. Enchantments with other card types, such as enchantment creatures, will also cause constellation abilities to trigger.

Protean Thaumaturge’s ability causes it to become a copy indefinitely. It doesn’t expire during the cleanup step or if the target creature leaves the battlefield after the ability has resolved.

An Aura spell that has an illegal target when it tries to resolve doesn’t resolve and is instead put into its owner’s graveyard. It doesn’t enter the battlefield, so constellation abilities don’t trigger.

If an effect begins to apply to Protean Thaumaturge before it becomes a copy of another creature, that effect will continue to apply.

Protean Thaumaturge copies the printed values of the target creature, plus any copy effects that have been applied to it. It won’t copy counters on that creature or effects that have changed its power, toughness, types, color, or so on. Notably, it won’t copy effects that made the target creature become a creature.

If an enchantment creature enters the battlefield under your control, Protean Thaumaturge’s ability can target it.

If Protean Thaumaturge copies a creature that’s copying something else, it will become whatever the target is copying.