Over the years I have created numerous websites using Muse. I cannot approach clients who have spent good money on these sites to redevelop them in another software. Will Adobe insure us that the latest version will continue to function for at least 3 years ahead? Are there concerns that newer Mac operating systems might interfere with Muse site operation?
"Will Adobe insure us that the latest version will continue to function for at least 3 years ahead?"
Absolutely not. Nobody can predict how long your Muse sites will last. The next browser updates could kill them. We just don't know.
Adobe first announced the Muse end of life in 2018. Muse has NOT been updated since and never will be updated. All product support has ended. And Adobe staff no longer monitor this space. Muse is dead. Use it at your own risk.
"Are there concerns that newer Mac operating systems might interfere with Muse site operation?"
Yes, absolutely there are concerns when a new OS comes out. It might work or it might not. Or it might work for a while until the next update and then stop working. Upgrade at your own risk.
-- Adobe Brackets (open source) - http://brackets.io/
-- Adobe Dreamweaver CC - https://www.adobe.com/products/dreamweaver.html
-- Pinegrow - https://pinegrow.com/
-- Visual Studio Code (open source) - https://code.visualstudio.com/
It works great on macOS Big Sur, no issues for me.
...except your icons which will never be updated.