I do not own Shingeki no Kyojin
Telepathic connection established between people was not supposed to be affected by spatial distance but rather by thoughts and familiarity. Having said that, its natural to think of people in your sight first so that wasn't strictly true.
The first effect was between the couples. Negativity inevitably breeds with time no matter how much they love each other and its much easier to notice them than positive thoughts. The period was known for mass separation of couples and that was still a decent scenario. In the some of the worst cases, people committed suicide. The situation between parents and children was much better but their were some disastrous examples there too.
It also meant that people did not take advantage of the most ridiculous effect of this event, the ability to talk to the deceased ancestors. They only talked to the recently diseased that they cared about. The exceptions were the titan shifters, Willy Tybur and Hange. Knowledge of the ancestors was too big a treasure to just ignore, but only for those who thought to look for it.
Mr. Hoover was lying in the hospital. Originally he would have heard of his son's death and lost his will to live eventually. The fact that he could converse with his dead son gave him strength to pull through. It still became a mental illness eventually though and he committed suicide to join his son in the paths.
Mr. Leonhart was waiting for his daughter to return when he felt her presence, physically trapped inside a crystal of her own making and unable to escape. He could not possibly rescue her with his damaged leg, ironic as she was the one to damage it. He had no choice but to report it to the Marley's generals. Unfortunately the telepathic connection did not work on them so he did not realize the mistake he was making. Despite its progress, Marley did not have precision weaponry to break the crystal anymore than Paradis did, so they had to rely on the Jaw titan. Even it had no way to safely recover the person inside the crystal so Annie's death was pretty much guaranteed. Only founding titan could have released her hardening.
Karina Brown along with Gabi Brown and her family had come to receive Reiner. Their thought process was the same, at least on the surface thoughts so there was no conflict. All of that changed when they saw Reiner, even from the surface they could see that his mind had been split into two. Gabi could not understand why he would feel so much pain from killing those worthless devils. She focused to get deeper into his mind. Karina on the other hand was completely devastated as the lies she had been telling herself for so long had fallen apart. The islanders weren't devils. Killing them while living among them had turned her son suicidal and she was the cause of it. Reiner knew they knew but at this point he had stopped caring. From what he knew, Marley would strip his armor by killing him even if his mind could recover. There was no point to anything anymore.
Zeke felt like he was really lucky. When he felt the sudden connection which was like all the information in the world flowing into his brain, he was already back with his grandparents. They were too traumatized to look deeply into him. He was also thankful that Pieck had moved on from him to Porco. That allowed him enough isolation to rearrange his thoughts and learn to keep secrets like euthanasia plan off the surface. What he didn't realize was that there were two men obsessed with him enough to observe him even from a distance at that time, Levi and Connie.
Armin felt like he had just awoken from a very long dream. He used to have a crush on Annie, not that it had stopped him from betraying her for his best friends and comrades. What exactly had changed since then? He realized just how much his feelings had bloated up due to Bertholt, now that he was free from it. He had even forgotten the reason why he had joined military to begin with. It wasn't just to be with Mikasa and Eren, it was the death of his grandfather. How could he have forgotten everything that Annie did? He had started to empathize with her thinking he was just as sinful but those were Bert's feelings. He had barely killed, saving Jean from Kenny's stooge was the highlight of his life and the result was him vomiting. If he couldn't even kill in self-defense like Jean, then he would be a saint rather than a human. Even so he did not want to be like Eren and think of only fighting and killing. There had to be other paths. With this connection between Eldians, new possibilities had arisen. He would do something he hadn't done since eating Bertholt. He would think. With his brain.
Just when Armin's obsession came undone, everyone else's came to the forefront. Mikasa with Eren, Jean with the death of Marco, Connie and Levi with Zeke, Historia with Ymir to name a few. The only person with a healthy obsession was Sasha for food. Meanwhile the thoughts of population were mixing. Those who were brain washed and those weren't and had legitimate reason to hate Marley had their thoughts start to mix like fruit juice in water. Initially they only saw each other as pets and traitors, they could now understand each other. Those who hated the island devils for a long time began to understand what really happened and that their memories were stolen. The people of paradis island also began to understand the hatred that the world had for them.
This was the purpose of Ragnarok connection. To remove all lies and barrier and make people understand each other to arrive at a single answer. The answer may not even be right or good in any way but it would be the answer of the world. Unfortunately the connection could only be extended to Eldians so this would not be the solution to everything.