Is a non-isolated power supply a good/safe option for "inside the case" Arduino / ESP01 / ESP32 / whatever control using the appliance's PS?
There is only one 'good' reason for using a non-isolated power supply - because you want to get the unit price down as low as possible for mass production.
But you are talking about using an Arduino / ESP01 / ESP32, which screams 'hobbyist project'. In this application it is likely not safe, as the hobbyist will probably want to tinker with the device while powered up, but probably won't be fully aware of the dangers involved. Also the hobbyist's design and constructions skills may not be good enough to produce a safe product.
Non-isolated power supplies are actually quite tricky to design properly, particularly when they need to produce significant power at low voltage. The ESP32 can draw up to 230 mA. Supply voltage over 3.6 V will kill it. Getting this low voltage and high current without a transformer is difficult.
Fully isolated supplies are so cheap now that making a non-isolated supply that is safe for both the load and the maker/user is probably not worth the small cost saving. Factor in design/debugging resources and likely destroyed devices, and it could easily end up being more expensive.