I barely use my MacBook Pro but I very often get 100% CPU after it wakes up – although it’s not only Safari, very often it’s the indexer, and sometimes other odd system services.
But yep, the Safari thing happened once on my iMac Pro as well. Took about 20 minutes for it to stop, was pretty strange but I was curious and left it alone to see if it will stop by itself. It did.
About the second point: nope, never. Maybe you have an older Mac with an NVIDIA GPU?