It’s like a state licensing board, same as for beer sales or beauticians or nurses.
Lawyers are just treated differently.
Ramsey v. BD. OF PRO. RESP., 771 SW 2d 116 - Tenn: Supreme Court 1989 - Google Scholar
There’s a lengthy discussion near the middle of this case of how TN applies 1A to lawyers and why it is different. It starts with “In dealing with First Amendment questions…”
In this case, attorney criticized the judge during trial. Speech was protected, but IIRC the court sets forth some caveats like “good faith” and “misrepresent.”