Are there any canon indications that an Avatar's personality is influenced by their previous life?

Question

Anecdotally, there are several examples we can point to of an Avatar's personality being a reaction to, or otherwise influenced by, the life experiences of their immediate predecessor. For example,

• Roku's life as the Avatar was deeply pained by the conflict it created with his best friend, Fire Lord Sozin, a conflict which ended up directly causing Roku's death. Then, Roku was immediately followed by Aang, who had a deep, instinctive desire not to be the Avatar, a fear/desire so strong he actually ran away from home to escape it.
• Aang eventually overcame his fear of being the Avatar when he was forced to fight Phoenix King Ozai, at which time he became more willing to engage in direct confrontations (such as we see during his handling of Yakone) rather than evasion and misdirecton. Then, Aang was immediately followed by Korra, whose first instinct is always direct physical confrontation, as though she was instinctively preparing to be a wartime Avatar early in life.

One might even make a connection between Avatar Kyoshi’s head-on confrontational style (and the negative reactions we’ve seen it inspire in the Earth Kingdom), with her successor Roku’s more passive stance toward Sozin’s ambitions, which seem to have amounted to one fight in the palace followed by decades of avoidance.

Obviously some of this has to do with the elemental orientations of each Avatar, (airbenders are famously evasive, while waterbenders seem more forceful in general, etc), and the connections could easily be explained away as coincidence or narrative symmetry.

But given the emphasis on past lives in the Avatar narrative, is there any comment made (in the shows or the comics, or by the showrunners) about whether the experiences of one Avatar will influence the style/personality of the next?

Answer 1

No, there are none. There is no mention of personalities being shared between avatars, aside from the toys used to determine who the avatar is. When Aang would go into the avatar state in ATLA, the only adjective I would describe of him and all the avatars together would be: wrathful.

Of course, the actions of the previous Avatar go a long way into determining the circumstances of the next Avatar's birth and childhood. Avatar Yang-Chen was an extremely effective Avatar, and so Avatar Kuruk grew up with the world in an era of peace and joy. This may have left him unprepared to deal with Koh the Facestealer when it kidnapped Kuruk's bride. Avatar Roku's failure to stop the Fire Nation from unleashing war on the rest of the world lead to Aang's training being accelerated, him running away from the mounting responsibilities, and being trapped in ice for 100 years. Aang's own experiences caused him to arrange for the next Avatar to be cloistered away from the world in safety, but much like Kuruk before her, this might have not done Korra any favours when it came time for her to deal with real world threats.