Does the UK government S1 healthcare form cover Turkey?

The S1 form is officially called:
“Certificate of entitlement to healthcare in another EEA country or Switzerland.”

No — a UK S1 form does not cover healthcare in Turkey.

Where an S1 form works
A UK-issued S1 certificate only gives healthcare cover in:
EU countries
EEA countries (Norway, Iceland, Liechtenstein)
Switzerland

If you live in one of those countries, the S1 allows you to access that country’s state healthcare system as if you were a local, with the UK paying the cost.

Turkey
Turkey is not part of the EU/EEA or Switzerland, so:
An S1 cannot be registered in Turkey
The UK government will not fund your healthcare there via S1.

UK pensioners or residents in Turkey must arrange their own health insurance or use the Turkish system privately

What UK residents in Turkey usually do
People living in Turkey generally rely on one of these instead:
Turkish private health insurance (often required for residence permits).
SGK (Turkey’s state health insurance) if eligible and enrolled.
Private healthcare paid directly.

Important note for UK pensioners
Many UK pensioners living in Turkey expect the S1 to work because it does in Spain, France, Portugal, etc. But it doesn’t apply to Turkey because there is no reciprocal healthcare agreement of that type with the UK.