I think player personalities should also depend on a hidden trait named "Pragmatism" which indicates how self-aware players are and their overall knowledge of football mechanics. I think it is pretty realistic because - and as a Juventus fan I can tell - there are players who are more aware of underperforming in a certain system or team and others who are less and just play without overthinking much.
Players with high pragmatism should work like:
they're more likely to transfer to teams in which they're more likely to play or develop, or have specific club values or policies they consider as important, or play with a tactical system they think favours them, rather than just reputation or participation to continental competitions. For example Haaland turned down Juventus for Salzburg back in the day because he thought he wouldn't have gotten enough play time nor developed as much as he did.
they're more likely to have a stronger opinion on each issue, such as tactics, results, training, playing in an unusual position, other players being unhappy, youngsters, etc. This might be either positive or negative.
when asked to suggest a staff member or a player to add to the team, they're more likely to suggest a better player/staff member, more likely to suggest a name rather than saying "I can't think of anyone", and more likely to suggest someone they have never met.
they're more likely to make reasonable decisions, for example they only turn unhappy if they have a good reason to, rather than being carried out by emotions. In the case of transfers, they're more likely to become unhappy if they're negated a move to a team with higher possibilities of developing (better facilities, more play time, more suited league and so on), rather than a move to a big team or a team they support. This does not increase or decrease the chance of a player being unhappy (it depends on the other attributes)
they're more likely to become better staff members after retirement
they're more likely to work smarter (rather than harder, the case with professionalism) during training or while recovering from an injury
they have a better understanding of tactics, instructions, and the rest of the squad (depth, quality, transfers being positive/negative)
they're more likely to discuss technical aspects of football and the club during press conferences
Players with low pragmatism, instead:
are more likely to be driven by emotions while taking decisions
are more likely to follow the majority, or influential players, or the manager as long as they have positive opinions of them
are more likely to suggest friends or no one at all when asked about a potential player or staff member appointment
are more likely to miss key players who were sold, even if they got replaced or left with a really good deal for the club
are less likely to understand if they're training or playing well or not, and the reasons behind their good/bad performances. Same with improving/declining and good/bad conduct
are less likely to change their opinion of something as soon as they formed one, even if the scenario changes. For example, a player with low pragmatism can form a positive/negative opinion of a new manager, but become more stubborn in changing their opinion if they already think of someone positively or negatively. Low pragmatism players also start out with better opinions of players and staff with a high reputation.
Once players retire, pragmatism increases their staff attributes but it isn't as important for as staff member as it is for a player. It does have the following effects:
more likely to find the right solution while the club is struggling
more likely to either use formations or instructions that are different than his preferred ones, or find better ways to adapt players to their tactics, if strictly necessary. They will always prefer the 2nd option over the 1st.
more likely to work better with the club's finances, only spending in the areas that they most need and only make exceptions for players they think to be bargains or really good
more likely to change reports on a player's ability/potential (if they're scouts), or a player's fitness status (if they're physios), after obtaining further knowledge of the situation. (Idk about this really, just wanted to give it a use for scouts and physios)
EDIT: pragmatic staff is also more likely to hire/sign "unprecedented" staff members/players, rather than going for players/staff they are friends with or already cooperated with before, if needed. They will also be less likely to complain if a player/staff member they had a good relationship with leaves or gets his transfer/appointment vetoed or blocked.
Pragmatism could also possibly define new media handling styles, it is rather easy for extremely pragmatic/non-pragmatic players to be recognized from press conferences in real life. I wouldn't add new personalities though.