Restart Requirement for Google Chrome/MS Edge. Are Reboots required to complete Web Browser updates?

I have a requirement to update Google Chrome and Microsoft Edge updates on several servers. Listed below are the patches.

Microsoft Edge Stable Build 119.0.2151.97 Available (x64)
Google Chrome 119.0.6045.200 Available

Both patches may require a restart to complete. Are Reboots required to complete Web Browser updates? What issues would there be if the servers are not rebooted after the patches are applied?