I consider myself an open-minded person; I have LGBTQ+ friends, some of them very very close. I identify myself as male and heterosexual... in my country, June is also considered "pride month"...
However (and this surely is not a trivial topic and surely one with different opinions), I dislike a bit the idea of a "pride month", hear me out before assuming or judging... The real acknowledgment is made each day, every day, by including and accepting people as they are regardless of orientation. We are in a professional environment, and the only judgment we should have here is precisely that: the professional capabilities and skills of each person
It shouldn't matter how someone identifies sexually or in gender. It should matter if a person is capable of doing their job, and doing it well.
Besides, the whole idea of a "pride month" is quite honestly a bit of marketing move; what happens when June ends? Exactly, everyone forgets about that and the pride flags are removed and life goes on... to me, that seems phony and pretentious (like, "hey look, I'm LGBTQ+ friendly, say how great I am").
One should be proud of yourself each day every day, not only for a month.
Your post tells us that you don't identify as LGBTQ+, so technically it's not "your" month... it's best to avoid mixing personal/sexual/gender things with job/professional things... even more if you are a manager.
You keep supporting and being open-minded, and lead with example and inclusiveness; but I would avoid sending an email or similar "just" because it's pride month... what about the other months? Do you stop being open-minded or inclusive during those months?
P.D.: I think this logic can be extended to other dates like Women's Day, etc... should we only celebrate women and mothers one day each year? Nope... and that's exactly why I feel this is more of a marketing move rather than genuine interest in those groups.
Yes, it's important to remember and celebrate those groups. It's part of the struggle those groups have gone through, and having a date/month is a way of remembering the strife and that we should continue fighting for equality and inclusiveness...
But be aware not to take it lightly and forget about all this the moment that day/month ends, as that completely goes against the strife and the whole point of being inclusive.