The secret about the New Rules is that there are no New Rules. The focus of what's more important now than before shifts, but there aren't any new rules.
The rules of getting a new job, being promoted, achieving success haven't changed. The tools and methods have changed - LinkedIn vs Monster, showing up in person vs a TEAMS link, navy blue suite with a watch/string or pearls vs business professional relaxed from the shoulders up, resume with your objectives vs bullets of your skills and achievements - change of methods but the substance/content YOU are still the key component.
Don't overthink the New Rules, they aren't that new. You've been doing this way for a while, you just didn't focus on your soft skills as much as you do now. Now you focus on what you bring to the table and where your skills will bring value, as opposed to before you were vague just hoping to get in the door. What you showcase in your LinkedIn profile and resume isn't what it was 3 years ago, but what you have to offer is still just as golden as it was then.
The New Rule....... Same rules different methods.