As of today (2023-01-07), "habemus dicentis" is the translation provided by Google Translate when you type in the phrase "we have a speaker". Curiously, if you type in "We have a speaker" (capital "W"), you get something closer to your suggestion: "Habemus orator."
As anyone with any experience with Latin Google Translate shouldn't be surprised to hear, neither translation is correct. "Habemus" requires the accusative. Orator is nominative and doesn't fit at all. As for the first, even the most generous interpretation--which parses dicentis as an accusative plural--yields, "We have [people who are] speaking." I'm not aware of any context in which the participle dicens has the same meaning as the political function of a "speaker," and (more obviously) there is only one. It seems pretty clear that someone without any knowledge of Latin plugged this into Google Translate and made it a headline.
My suggestion would be to use praeses, which is used even in modern contexts to refer to the presiding officer of a committee. The phrase would thus be:
Habemus praesidem.
The one downside I see is that praeses is also a plausible translation for a "president." According to a comment from Joonas, though, some neo-Latin speakers distinguish praeses (head of a committee) from praesidens (head of state).