Reach out without the cringe.
The reason cold outreach reads badly is almost always that it could have been sent to anybody. Six questions, one of which is a real detail about them, and you have a draft that could only have been sent to one person.
Questions people ask
How do I write a cold outreach email that gets a reply?
Make it obvious it could not have been sent to anybody else. One real detail about the person, one sentence on who you are, and one ask small enough to say yes to. Length is not the problem; interchangeability is.
What should I actually ask for?
Something small enough that saying yes costs almost nothing. Fifteen minutes with two questions ready gets answered far more often than an open request for a chat, because the second one has no visible end.