Could a public school teacher start a prayer group for teachers in the US?

I’m familiar with the wall of separation between Church and State and the precedent set by Engel v. Vitale. However I’m unaware of whether that’d apply to state employees within their own remit. For instance there are prayers held in the Senate.

Somewhat inspired by this song, too.

My WAG from growing up in the US and being exposed to some church/state analysis says that it would have to be clear that participation is 100% voluntary and that supervisors are not going to “encourage” teachers to attend or make personnel decisions based on who does or does not attend. Unfortunately bias can make us do that.