Sentience cannot be proven, since it is, by definition, a subjective sense of self.
But in terms of what has been said about droids in official materials:
There are different classes of droid, some of which are more sentient than others, and droids can gain sentience over time, which is why the empire regularly wipes their droids
Do they ever actually do anything prove droids are sentient in Star Wars?
Sentience cannot be proven, since it is, by definition, a subjective sense of self.
But in terms of what has been said about droids in official materials:
There are different classes of droid, some of which are more sentient than others, and droids can gain sentience over time, which is why the empire regularly wipes their droids
This is anti-droid propaganda, all droids in Star Wars are sentient
I hate this. Just have them being cute, bumbling robots.
That works. They’re all just movie magic at the end of the day
Do they ever actually do anything to prove biological life forms such as humans are sentient in Star Wars?
No.
Droids have personalities, hopes, dreams, fears, preferences and awareness of their own thoughts as well as awareness of their own mortality.