In my opinion, just is often used in an opposite way to condescension. "Just do x" is often used to assume you would do a more difficult task in the easier task's place. So, for instance, if you were to use an automation tool, I'd likely describe the last instruction on how to automate it as something like, "Just click the button and everything is running!"
"Simply", however, usually isn't used this way.
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I don't know if "just" is in the same league as the other words.
The word "simply" definitely is condescending, and "just" can be used that way, but "just" can be used in many natural ways.
With that said, it usually isn't necessary.
In my opinion, just is often used in an opposite way to condescension. "Just do x" is often used to assume you would do a more difficult task in the easier task's place. So, for instance, if you were to use an automation tool, I'd likely describe the last instruction on how to automate it as something like, "Just click the button and everything is running!"
"Simply", however, usually isn't used this way.