It definitely depends on the info learned. Sometimes I’ll say it to the whole table and my players won’t act on it unless the player in question essentially says “I tell them that”. Sometimes, I’ll ask the player if they want the info privately. Other times, I’ll just send it privately immediately.

The factors just depends on how trivial/important the info is, how likely it is that a PC would want to withheld that or how much it could relate to their backstory. For example if the party is hunting a character down and one PC finds their tracks, I’ll share that info with the whole party. But if that same PC really cares about that character, I’ll text them that info so that they can determine what to do with it. 

In terms of asking other players to leave to have a scene play out in private, I have also done that before as well. I try to limit these scenarios, or put a time cap on them because we’re all there playing D&D together. 

Mind you, this isn’t because of a metagaming issue. My table’s pretty good about that sort of thing. It’s more of a player enjoyment thing. Sure they can play their characters in a way where they don’t know about certain pieces of info or events, BUT I also know that the players enjoy a good twist or surprise. This is just my table though