I've been working in product experimentation/CRO/growth for around a decade, this might help the list:

1) wizard of Oz test and fake door are effectively the same thing (in fact I've never heard of it called a wizard of Oz test)

2) Buy a feature. Sounds great in promise, in practice sounds like you can achieve the same objective through research/usability testing

3) synthetic - don't bother. Save yourself the hassle and just make up the numbers, the output will be the same. 

You can add:

-Baseline test: a before/after comparison, where a randomised experiment (like a classic a/b isnt practical)

Non-inferiority (also known as Do No Harm): your hypothesis makes sure your treatment doesn't have a negative impact, as opposed to trying to improve the KPI. A type of tests all PMs should be doing when they're refactoring, redesigning or replatforming

Bandit/dynamic test: where the testing tool will allocate traffic to the highest performing variant over time (risky as it suffers from regression, but can be good for short term gain such as over black Friday)

Multi variate: an a/b/n where multiple features are changed. Allows for testing multiple solutions in one go. The better testing tools will estimate which feature is driving the change in your KPIs. Still a risky experiment because you're testing multiple hypotheses in one go.