He’s mentally tough, it’s just that his weak point is his ego which isn’t surprising since it’s also the source of his strength.
Vegetas reaction to Broly is not canon and you know this. Non canon material gets no play on any court. He’s fought people that he knew were stronger than him without fear so that don’t even add up. The Legendary Super Saiyan is like a religious figure to Vegeta. So it’s less about Broly being strong and more about who he thought Broly was.
It’s like Piccolo losing his shyt when he met Supreme Kai. Piccolo was probably as strong as SK was at that time but Piccolo sensing that Supreme Kai was a god is what freaked him out. He recognized him as a deity and backed down.
Vegeta didn’t run from Frieza’s fade, he’s the main one who stepped to Frieza

he just got washed like everyone did, including Goku who got to run it back after going ssj. Same as 18, Vegeta is the one who stepped up to fight. Again, like everyone else, he got washed. Goku lost to a much weaker android because he was sick but even if he had been at full power, 18 would’ve done Goku even dirtier because at that point, Vegeta was stronger as a super saiyan than Goku was. She was just stronger than either of them.
And while you said Goku never hesitated, he flat out DUCKED Cell when they met the first time and did so specifically because he knew he was weaker. Don’t forget that. He saved Tien, begged Cell for more time because he isn’t strong enough and when Cell said nah son, we can fight right now, Goku ran. So saying Goku never hesitated when he’s deliberately ducked a fade is a miss.