After installing Veeam 9.5 Update 3a and simultaneous upgrade of vSphere from 6.5 to 6.7 Veeam vSphere Web Client Plugin might stop working for vSphere HTML5 Web Client. However it is still operational in vSphere Flash/Flex Web Client.
The issue is only reproducible in case the plugin was present on the vCenter prior to upgrade. The installation logs on vSphere side will show:
[<date and time>] [INFO ] vc-extensionmanager-pool-<id> 70000019 100003 200001 com.vmware.vise.extensionfw.ExtensionManager Plugin package com.veeam.backupui.VeeamBackupUi:126.96.36.1992 was not deployed because attribute type="html" is missing, which is normal if this is a Flex plugin