Coal Stoker — ruling 1

If a nontoken creature enters the battlefield as a copy of this creature, the copy's enters-the-battlefield ability will still trigger as long as you cast the spell that became that nontoken creature from your hand.

Coal Stoker — ruling 2

If a token is created that's a copy of Coal Stoker, the token wasn't cast, and Coal Stoker's ability won't trigger. Similarly, if an effect copies Coal Stoker while it's on the stack, the copy becomes a token, but the copy was created on the stack and not cast from your hand, so the ability won't trigger in that case either.

Coal Stoker — ruling 3

Coal Stoker's ability isn't a mana ability. It uses the stack and can be responded to.

Coal Stoker : règles, fonctionnement et interactions (MTG)

Coal Stoker is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

When this creature enters, if you cast it from your hand, add .

How it works : Coal Stoker

Original English text — Wizards of the Coast / Scryfall

#1December 8, 2022· Wizards of the Coast
If a nontoken creature enters the battlefield as a copy of this creature, the copy's enters-the-battlefield ability will still trigger as long as you cast the spell that became that nontoken creature from your hand.
No other card is named in this ruling.
#2December 8, 2022· Wizards of the Coast
If a token is created that's a copy of Coal Stoker, the token wasn't cast, and Coal Stoker's ability won't trigger. Similarly, if an effect copies Coal Stoker while it's on the stack, the copy becomes a token, but the copy was created on the stack and not cast from your hand, so the ability won't trigger in that case either.
No other card is named in this ruling.
#3December 8, 2022· Wizards of the Coast
Coal Stoker's ability isn't a mana ability. It uses the stack and can be responded to.
No other card is named in this ruling.