I don't feel that "soft skills" are sought or even desired in an engineer -- I'm only ever asked about some certain framework or technique or algorithm (lol), not even tangential open-ended stuff like "hey how would you approach a customer complaining about X" or "How would you prioritize technical debt vs features in a product's lifecycle?" or, heck, even something fun and off the wall like "you've lost your wallet in a foreign country -- now what?"
I'm glad your startup experience was useful in your own search. Best of luck on your new endeavor! :)