What is the right way to float a home lab?
You can't float everything without an isolation transformer - the neutral will be connected to ground at the entry into the building. For safety any class I equipment does need to remain grounded, in my lab I have an isolation transformer only for the equipment under test, the scope and power supplies still have the case grounds, and are tolerant of the inputs/outputs floating up to 50V from ground (per their manuals). If I need to measure high side DC stuff, I can connect the high side to the scope ground (since the isolation transformer allows that offset) but a differential probe is still needed for measuring small signals with a large offset - it's far cheaper to buy one than smoke an oscilloscope