Both options exist. You can get some straight plunge bits for your router, or they make drill guides, which are kind of like a mini portable drill press that can be used with any drill - https://www.amazon.com/Milescraft-1318-DrillMate-Drill-Guide/dp/B014A1Z92I?th=1
I use the recessed door sensors as well. They work great, but damn that is a tricky hole to drill! Luckily I have old-school wood doors, I’m not sure how you’d do steel or fiberglass. I found a portable drill guide indispensable for the task (Milescraft 1318 DrillMate Portable Drill Guide - https://www.amazon.com/dp/B014A1Z92I/).