how does a search engine measure experience (if they wanted to)
They're not looking at your author bio, I promise you.
It's all math. When you vectorize the entire internet, the "experience" sites will cluster together. Reddit, Forums, reviews, etc. There will also be a cluster of non-experience: wikipedia, dictionaries, news, etc.
The engines just see what cluster's centroid is closer to your website.
They don't need you to spell out experience - because your site is an entity, and it fits on a knowledge graph - and they can compare it to other "experts" on the same knowledge graph.
Hope that helps.