One of two oldest friends, Jack Crusher.

First time we hear about him he's already dead.

Second of the two oldest friends, Walker Keel.

His ship gets blown up in the same episode he was introduced in.

Alright, how about another old friend, captain Donald Varley?

Uh... His ship blew up. Right in front of eyes of the TNG crew.

It sounds about right that character who lost every best friend so far subconsciously connected their deaths to his friendship with them and figured it's better to keep people at a distance, which would, in his mind, either protect them entirely from the same fate, or at least make it a little bit less painful for him.

harry kim and wesley crusher had a toxic rivalry in the academy. they might or might not have hatefucked about it at some point

the crew of the vancouver found out why beverly quit starfleet when they looked for her during the nova crisis and they just never told anyone because it was none of their business. also dr. noum was onboard and that's why he knows where to find beverly in prodigy

janeway briefly went to migleemo, who used to be a competent professional, for therapy after voyager and the experience broke him psychologically

jack ransom is closely related to rudy ransom, the captain of the equinox

julian bashir sent a letter of recommendation for dal to be accepted into the academy and it wasn't just janeway batting for him

sisko is responsible for sending barniss frex to his outpost position after he fumbled his post during the dominion war

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Jack Crusher

He is dead way before the series started like 10 years before and we see him like two times in the series and manages to completely control 3 characters narratives who's actions actively affect those around them.

Character number 1:

Wesley Crusher

His entire arc is him working towards doing the same thing his father did joining the academy and becoming a captain and eventually he has to come to terms that he doesn't have to follow that path because it isn't his it's someone who the universe let him barely know. He barely even remembers him but does that stop him. No. When Riker asks him at farpoint how he knows him it's in relation to his dad's death. He could have said former family friend but no he hangs up on the thing he still remembers. Not him being the family friend but him being passively resentful to Picard about destroying his family. He's about 16-17 when he finally talks to Picard about it admitting he stayed resentful for a while afterwards about his dad's death (and that was forced he was actively avoiding talking about his feelings about it) and even his psychological evaluation for the academy (which was kinda harsh like go make the same decision that caused your dad's death were not explaining this is the test till afterwards) explained that even 10 years after his death he still is incredibly worried about making the same command decision that killed his father. When he has pretty much given up on the academy by season 7 the only reason he stops is because he was told by a hallucination of his father to stop following his path. He only stopped because he was told to by his spirit visiting him and the only time he speaks to him after his death. He lives in his dead fathers shadow until he eventually realises that he doesn't want it. There's a chance he never even wanted Starfleet he just happed to like being helpful and like helping in engineering and being on the bridge and its highly possible every adult around him pushed him to follow in his father's footsteps until he himself believed that was what he wanted because that's what everyone told him he wanted(That entire last bit is speculation but wouldn't surprise me). He lives that life of the ghost haunting his narrative. Wesley affects the narrative every TNG episode he's focused in and nearly every time it's because of him being Jacks son or him following Jack's path. Wesley continues to affect the narrative in prodigy because he chose to go against the path layed out and become a traveller.

Beverley Crusher:

Jacks death left her to look after a child all on her own and her actions had to take that into account that she didn't have him to go to anymore as her backup and Picard runs off in shame. She accepts the posting to enterprise and he only realises it's Wesley due to her and one of the first things she brings up in the conversation was that the last time they saw him was getting told about Jack's death(must've been a bit weird on the bridge like "oh that's how they know each other. Oh wow."). During that episode he even offers to support her moving ships and she points out that she chose the ship knowing full well he was captaining it and his past. She even names her second child Jack even though he's been dead all these years because she is still tied to him even though it's Picard's son. Her episode where everyone disappears can also be linked to him through the fact that everyone goes and that she entirely fears it and forgetting them because she already lost her husband. She lost him all those years ago and still fears losing people still because she knows how easy it is especially in Starfleet. She continues to affect the narrative in both TNG with her multiple times being linked in relation to her relationship with Jack especially by Picard and in Picard with he actions with her son directly named after him.

Jean Luc Picard:

His actions are based off of his guilt about repeating the same mistakes. He refused there to be another Crushers death on his hands. When he first met Wesley on the bridge he tells him about his dad after he ran away from them for years because he blamed himself for causing it. He says he'll support a transfer for Beverley so she wouldn't be on the same ship as him due to his involvement in her husbands death. He repeatedly saved Wesley and Beverley even if technically not allowed by Starfleet's rules and regulations partially due to his guilt about one death making sure he doesn't have to come to the other and tell them about the others death. His reaction to finding out that Wesley had resented him showed that still there was always going to be the lingering presence even after being told he doesn't resent him anymore.It's revealed that he loved Beverley for a while but never told her because of her and Jack's relationship and after his death it made him feel even more guilty especially how he went with her to identify the body and confirm his death. His actions affect the series and how he considers his orders during his Starfleet career affecting multiple series.

In conclusion the actions of these characters affect multiple series and films and those actions are affected by one character we mostly know the name of and who he was in relation to who he was to others.