It is perhaps me, but I think there is confusion re what personal branding means in this thread.
Some are interpreting it as the brand for a small business that you own personally, but that is not how I interpret the term. I interpret that it is your brand as a person, that is shares the story of your personal accomplishments, goals, plans, interests and causes. On your personal branding site might be your resume (perhaps), interests such as hobbies, causes or volunteer activities, etc.
Now in a few cases of celebrities, entertainers, influencers, etc., the same site might be both their personal branding site and their business website, but for most they are something entirely different.
As I (possibly incorrectly) interpret it, the site where I promote, sell and talk about domain names is not my personal branding site. For the domain promotion site I would probably not use .me, unless I was selling mainly .me domain names, or domain names primarily for personal branding, perhaps.
My personal branding site, which I don't have one, would include things like my resume if I was looking for work, a statement about things that are of interest to me, a link to my LinkedIn and Twitter, possibly some photos or artwork I wanted to share widely, links to organizations I volunteer with or feel strongly about, perhaps links to a few things that I wrote, especially opinion pieces. Some people use their LinkedIn profile as essentially their personal branding site.
To me for that sort of use, a strictly personal branding site, .me makes a lot of sense. Odds are you can hand reg some variant of your name, and the extension tells people it is probably a personal site. Descriptively accurate.
Bob