Clients trickle updates out over time and not at the exact same time. So using the "Check for Updates" to force current updates can be done by clients, but usually these updates to require a quit and reload, or reboot before the will completely spin up. As adam said as well they require certain level on onboard hardware to enable background blur.
As for sign out vs. restart. Sign out has some kind of extra cache clearing as I have seen it fix issues that regular reboots would not.
Also, Microsoft has said they are working on a way for us to manage deployments of Teams better so we should be able to wait for a release then make sure it gets pushed out when we want etc. or maybe some kind of release branch. I know they are working on it, no ETA published yet.