@ckangis, I'd look at the Rally Bar with Extension Mics in that Boardroom space. Sets you up nicely for Logitech's Sight (center of table camera/mic solution) coming mid-'23 as Sight will require Rally Bar (or Mini) for some more advanced features; like auto handoff of users between cameras as they focus their attention between fellow participants across the table and persons remotely on the display at front of room.
In the Theater you'd most likely want to look at Logitech's Roommate as it's meant to be dropped into a system where a DSP is needed for wireless mics, zoning out audio, etc. Supported partners include QSC, Biamp, Nureva, Shure, and continues to grow, but those relationships allow for easier access to resources with those vendors in addition to the confidence of knowing you'll be supported should anything odd arise. The camera could be a Logitech Rally Cam, Rally Bar (in USB mode) or any other supported 3rd party camera. FWIW, I find this type of environment funny for Zoom calls too, but with AMC now renting out their theaters for this very purpose, I suppose it's being adopted to a certain degree.
For the sake of transparency, I am currently a Logitech employee who was previously a TD at Crestron for the US West Coast. I've spent the better part of 20 years in the integration space, as an engineer and programmer.
Nathan Spear