VMware has just released updated information on this topic, which requires action for customers pre-vSphere 6.7 Update 1. Essentially, Flash which underpins the vSphere Web Client goes end of life in December this year and browsers will cease to support it. Customers will need to switch to the HTML5 client, which became feature complete with vSphere 6.7 Update 1. The recommendation is actually to upgrade to vCenter 6.7 Update 3 prior to December to avoid issues.
Blog post: – https://blogs.vmware.com/vsphere/2020/04/vsphere-web-client-support-beyond-adobe-flash-eol.html
KB Article: – https://kb.vmware.com/s/article/78589
vCloudburst Blog 