Technical sales, project management, or engineering services. These are often combined. You want something that puts you on the ground with the customer. They'll start asking you for technology/software advice if they like you. It helps if you like traveling.

Alternately, instead of starting a new career, you could ask friends and family for an introduction where they work and just go with your original idea of shadowing people. Most SMB owners I know would be happy to let a software developer analyze their process and brainstorm about useful software. Just give them a perpetual free license for helping you develop it. They might even be interested in helping you bootstrap it. Business owners are often looking for a good investment.

Being a dev is fine, but it usually means being in a small company. Alternatively, try to meet people in the company who aren't devs. Talk to sales, marketing, production, start small talk with who ever's in the breakroom, etc. Salespeople especially, love to talk :-)

Product Manager will let you know what people are requesting but sometimes the requester is a clueless manager.

Working tech support will tell you what real users are having trouble with and sometime they have really great ideas for features.