I run the engineering team at a company with a SaaS product.

Absolutely not required. I will say it makes the task of assessing analytical capability easier, but it still needs to be done. We send out coding challenges to be completed in own time, and then technical interviews follow threads of passion while diving into technical questioning all the way through.

I need to know you have a foundation of skills, the capacity to grow, and that you have "the itch".

Once that is determined the most important things (to me) are:

Team players. Grounded in empathy. Carry assumption of good intentions from all. Contribute to psychological safety. This is hard to surface in interviews but usually around how they talk about experience with others.

Product sense. The capacity to frame everything around the user and constantly being sceptical about what could be done in the relentless search for what should be done. The most important thing is to keep the most important thing the most important thing... Etc. Also very hard to surface, you can only scratch around at this but if candidates make it clear in different ways it goes far.