I left the UK to reside in Thailand in 2005 and immediately informed HMRC that I was no longer a UK resident.
Seventeen years later (2022) I claimed my State Pension. It was, and still is, paid at the rate applicable in 2022. So, it appears that the rate applied is that on the date of the claim - not the date of changing country of residence.
Just to add - Deferring one's claim will also increase the weekly pension payment. According to https://www.gov.uk/deferring-state-pension/what-you-get the weekly pension payment increases by 5.8% for each year it is deferred.
However, the extra payment is also frozen (if you reside in Thailand etc.)
Edit: Why can't we embed links to websites?