Warning: Spoilers Off applies to these pages. Proceed at your own risk.
In "Amamiya Family Reunion", Ren's parents are depicted as reasonable, loving parents who were forced to go through a really bad situation. In the author's notes, Vivvav described wanting to explore the idea of his parents not being terrible people.
The entirety of "Baby Sakamoto", but special mention goes to the artwork featured at the end, showing Ryuji and Hifumi asleep with their child.
Ren and Makoto having managed to be a couple for ten years, as of "Rules of Engagement", to the point where Ren's friends agree he should pop the question. And he does.
Offhand, Ren mentions that Makoto is still friends with Kanji, years after "The New Adventures of Buchimaru-kun".
The artwork◊ featured in "Good Cop, Bad Cop". It's simply adorable.
The artwork◊ for "the New Adventures of Buchimaru" depicts Makoto growing up with her beloved mascot character, from her wearing a Buchi-kun baby onesie to her present day pencil case, clearly depicting how many happy memories are tied together by Buchimaru.
"The Days Between" is full of these, for different characters comforting Ren, but special mention goes to Futaba's chapter.
"Sakamoto Mother's Day" highlights how Ryuji loves his mother, and the fact that the others are willing to help him out shows how much they respect that.
As an officer, Makoto can't wear her favorite headband on the job because criminals and lowlifes won't take her seriously. Ren knows this upsets her, so he commissioned an engagement ring with the same braiding as her headband to give her something to compensate.
Igor's interaction with Morgana in "Alleycat". Igor congratulates Morgana for his success and explains that while he had to create Morgana in haste, he created him as a person, not a tool. Igor then rewards Morgana by letting him back into the real world with a body again, giving him the gift of life.
Most of Rainy Day Visit is heartwarming, just a fluffy slice of life story. Most notably, the continued connection between Kanji and the adult Phantom Thieves, and the fact that Makoto and Ren will have a child in just a few months. Another moment is Morgana and Yoshio getting along famously, despite the buildup implying otherwise.
Meta example: While Vivvav does away with calling the protagonist "Akira Kurusu", they do it in style by writing a fic (Farewell To My False Self) to subtly nod at this. Taken further when Vivvav acknowledged that the trope pages didn't have to change Akira's name to Ren every time- but it was changed anyway. If Vivvav went through the trouble of editing old fics, readers could easily honor that and manage the trope page.
"The Shadows Linger" reveals that Yosuke and Labrys are now a couple. When Futaba mentions the goatee Yosuke has and how it looks bad on him, Labrys admits she doesn't like it either, but since Yosuke never asked her to make any changes to her appearance for him, she intends to show him the same respect.
Just about everything in "The Amamiya-Nijima Family", in which Ren and Makoto decide it's finally time to have kids. The rest of the gang immediately do whatever they can to help them get ready, including Sae giving them reassurance and advice, Ann and Shiho taking Makoto out shopping for maternity dresses, Haru and Morgana offering to come up with names, Yusuke painting the nursery, and Futaba and Hifumi giving Makoto a practice interview for when she has to apply for their child to go to preschool. By the end of it, Ren and Makoto have two children on their hands: Ryoko, their adopted child, and Hanami, their birth child.
Yusuke's role in particular is heartwarming for the sheer amount of enthusiasm he puts into painting and designing the nursery. Ren noted that Yusuke's eccentricity was what led Ryuji and Hifumi to not ask for his help when Yoshio was born, but it's clear that Yusuke wouldn't have it any other way. He even goes as far as to consider his latest work his "masterpiece".
Ren: "Yusuke, you remember that we asked you to keep it simple, right?"
Yusuke: "Simplicity is for paper cups! This is the home in which the child of two of the most important people in my life will slumber, will grow and become their own person to continue their parents tradition of excellence! How can you ask me to do anything but create my greatest work yet!?"
In "Hanami's Soldier", after hearing the story of Cadmus planting dragon teeth to grow an army, Hanami plants her lost baby tooth in a pot to grow her own soldier. Rather than break her spirits about things, Ren falls back into his Joker persona and hatches a plan. Over the course of several days, Ren replaced the tooth and created the illusion of a toy soldier growing out of the pot to his daughter's delight.