Writing As A Professional, In Public
You cannot fully separate the person writing from the person employed.
A teacher writing about teaching is not writing as a private individual who happens to have a job, however clearly the sidebar disclaims it. The authority of the writing comes from the role, which is what makes it worth reading, and it also means the role travels with the words. Readers connect the two. So do colleagues, students and families, sometimes years later, and the disclaimer does not undo the connection.
This does not mean the writing must be bland or cleared in advance. It means the professional context is a real feature of what you are doing and should be held in mind while drafting. Employers commonly have expectations about public communication by staff, and those expectations vary widely between organisations and sectors. They may be written down, they may be informal, and they may be more specific than you assume. The sensible order is to find out what applies to you before publishing, not in response to a conversation afterwards.
The practical consequence is a slight raising of care rather than a chilling of the whole enterprise. Most writing about your own practice sits comfortably inside any reasonable expectation. The friction arises at the edges, where description shades into complaint or where internal detail appears in public, and knowing where those edges are for your own situation is worth an hour of finding out. Obligations and institutional policies in this area exist, they differ, and checking is the writer's job.