Q1: Am I likely going to be able to successfully switch a video device through a USB 3.0 switch like these examples? If not, what is the primary technical reason? (assume that I am an electrical engineer with a networking background, but no direct experience with the tech details of USB.)
This should work and the switching should be no different than removing the USB devices physically from one computer and connecting them to the other.
Q2: Given that these devices are essentially switchable USB hubs, is
there any reason to choose the type B ports instead of the type A
ports?
You choose the one with the USB-B ports because USB-A ports as inputs violates the spec for connecting any USB 2.0 devices and is only allowed under USB 3.x when connecting USB-A host to USB-A host. Such cables for USB 3.x host to host connection by USB-A are somewhat of a specialty item, used for Windows and Linux kernel debugging for one. The USB switch with USB-A ports as inputs cannot meet the spec since the switch is not a USB 3.x host.
The only way this complies with the USB spec would be in a way that does not allow the use of USB devices, only connection to other USB hosts. If they mean "switch" like "Ethernet switch" where the switch is automatically diverting packets to their intended destination then maybe this somehow complies with the USB spec but that again does not match the intended use of plugging in USB 2.0 and USB 3.x devices.
If you are looking to switch mouse, keyboard, audio, and USB devices then I believe you are looking for a KVM switch, not a USB switch. Look for a KVM switch that allows for the switching of USB 3.x devices. Here's one example: https://www.startech.com/en-us/server-management/sv231dpu34k
That link is not an endorsement of the specific device. I used StarTech KVM switches before and they appear to work well enough. I don't have much experience with the competition to know if there is better stuff.
The KVM in "KVM switch" means keyboard, video, and mouse. These will switch video (HDMI, DisplayPort, VGA, or whatever) with the USB ports. It sounds like this might be useful for you, if not then it may still be a wise choice because these will have been built for your intended use and not for whatever use that UGreen device is for. The only use I see for that UGreen device is to separate people from their money and leave them with something that will likely not work, or not work and damage USB ports on computers.
If there were not so many junk USB switches out there then I might not be so against them. Because so many of them are junk I assume all of them are junk.