The Verdict: Not eligible
At 36 or over you are past every age cap on this scheme. Look at Skilled Worker, Global Talent, Innovator Founder or the UK Ancestry visa, which have no age limit.
The highest cap is 35, for Australian, Canadian, New Zealand and South Korean nationals; everyone else stops at 30. It is tested on the day you apply and there is no discretion.
The routes with no age cap:
Skilled Worker, if an employer will sponsor you in a graduate-level job. Global Talent, if you can be endorsed in research, the arts or digital technology, or hold a qualifying prize. Innovator Founder, if an approved body will endorse a new business you are building. The UK Ancestry visa, if you hold a Commonwealth nationality and a grandparent was born in the UK, the Channel Islands, the Isle of Man, or in what is now Ireland before 31 March 1922. Unlike this scheme, each counts towards settlement.