What is the position of science with regard to tulpas? Surely, if the phenomena exists, science must have encountered it an d have a stance wrt. it, right?

There no such thing as a position of science. Science is a process.

As far as Tuplas go, Tulpas are mainly about qualia. Qualia are by their nature but directly measureable. As a result a lot of scientists do shun research of qualia. Orthodox reductionists do try to explain qualia away whenever they can instead of trying to investigate them.

Western scientific education doesn't train it's scientists do be in control of their minds and that means that most they can't run experiments that require mental control and good awareness of their own minds.

They can invite some buddhist monk and investigate how that monk does his thing, but that doesn't allow for easy controlled experiments.

In that area even the easy questions seem to have little scientific investigation. Take heat development during particular types of meditation.

Ten years ago a scientists would have looked strangly at you for suggesting for heat development without movement but now we do know that the body can in principle do this in brown fat tissue.

There some small experiments that illustrate that a specific Tibetian technique can consistently produce heat but there no general science based theory that predicts when you would expect someone who meditate develops heat. It's even not clear whether it's really produced in brown fat tissue because adults have little of it.

Present thinking in medicine is rather: "How can we develop a drug that stimulates brown fat tissue to be active to help people lose weight?"

Tulpa need around 6 months of hard focused mental practice of 1 hours per day. That not something that you usually study in scientific studies.

If you look at another recent controversy on Lesswrong we even disagree whether mainstream science knows what losing weight is about. There a lot more scientific effort going into that question but it still isn't conclusively answered.

If you are looking at far out mental phenomena there no reason to expect that they are well investigated by scientists.