Do business class passengers get fast track immigration at Bangkok airport, or do you need to pay?

I’ve read that you can buy a fast-track service at Bangkok airport to skip the immigration queues.

Since I’m flying business class with Turkish Airlines to Bangkok, I’ve also heard that business class passengers might already be allowed to use the fast-track immigration lane for free just by showing their ticket.

Is that actually true, or do you still need to pay separately? And if it’s not included, how much does the fast-track service usually cost?