before Chara's death:

Sans, instead of being a royal scientist was a royal guard, near undyne's rank. Sans wasn't the most welcomed person in the Royal guard.

(Sans has the abilities of classic, but his "KR" works on anyone, and is controllable. Also know as AR-Arterial Retribution or in otherwords, the severest bleeding type.)

Around the time of Chara's death:

Chara devising a plan to free the monsters goes "too far", though he doesn't get Asriel involved.

Chara makes a plan: Kill a boss monster to get their soul to escape to the surface to get human souls...
that monster just happened to be sans.. and well, Chara lost.

Sans was very distraught after killing A Dreemur family member, and was kicked out of the royal guard.

the people of the underground followed the prophesy of
"An angel will descend from the surface world and save us all" So this death affected the whole of the population. (yes its from Deltarune)

Due to this, everyone loses hope, and the UT timeline things happen. Meanwhile, sans goes into hiding, though mostly at his house.

After Chara's death:

Sans:
Sans'es abilities have gotten heavily suppressed due to this tragedy.
Papyrus heavily helps him overcome all of this, and gets him to finally leave the house.
Sans find's the door of the Ruins and makes good friends with Toriel
(Toriel recognizes him due to the events that took place, unlike in undertale)
Toriel convinces sans to have a talk with Asgore to get on better terms with him. (right after sixth human fell)
it goes okay, and they don't severely hate eachother anymore.

Asriel:
After the Funeral Asriel becomes heavily depressed. he stays near Charas grave 24/7 wondering why this happened, and has a deep hatred towards sans.
Asriel spirals deeper and deeper into depression.. and.. things dont end well..

Undyne:
She holds a massive grudge against sans, revenge fueling her to always be on the lookout for him.
she would be the first always to investigate a sighting of sans, but she never overdid it like asriel.
after sans has the talk with Asgore, he goes to have a talk with Undyne and she promises not to hurt sans. but ever since, she hasn't dropped the massive grudge against sans.. but doesn't show it openly.

Papyrus:
Papyrus has always had a soft spot for sans, and when he found out sans was innocent he always pushed him to be better, ultimately saving sans from a bad fate.
Papyrus still strives to get into the royal guard, though he isn't as optimistic as UT paps, and lacks the motivation to make any puzzles
(He loves crossword puzzles for some reason.. lol)
and fights you head on. especially in genocide, as he isn't going easy on you now.
(papyrus has a negative version of him aswell though he never uses it fully in the geno fight. he uses it to stay alive for a final strike after going down.. something like the Neutral UT Undyne fight.)

Toriel & Asgore:
Their bad traits have been highly raised, though Toriel has a better mindset now because of sans. (nothing much to say about them for now, lol)