I have never paid income tax on my state pension, but saying that I don't even get the full amount
At the moment no one who has just the state pension as their only income pays income tax, even after the increase that is possible next year you still won't as it is below the tax threshold.
However, if the threshold is not increased in 2027 the pension may be above the threshold and tax charged on the pension above the threshold of £12,570.
Anyone who has a private or workplace pension does pay tax on that.