Shinji is a moon chef, and if measured by his favorability rating, his affection for Artoria is above 80.
Artoria, on the other hand, maintains a considerable level of favorability towards Shinji—about 70—due to his different behavior compared to other magus, his remarks during the King's banquet, and Scáthach's unintentional influence in the end.
With such a foundation, the communication between Shinji and Artoria is exceptionally smooth. The two seem to hit it off immediately, like old friends who haven't seen each other in years, talking until they lose track of time.
They talked about many things.
For instance, why is it that despite your body having been solidified by the Excalibur and Avalon, maintaining the form of a 154 cm tall girl even in Avalon, you now appear as a 173 cm tall mature woman with a chest circumference over 100 cm?
Answer: It's Merlin's doing. The Sword in the Stone was Merlin's creation, and solidifying Artoria's body was also his work. He can solidify it, and he can undo it. After receiving the message from the Counter Force and before responding to Shinji's summon, Merlin asked Artoria if she wanted to see what she would look like as an adult. Having already shed her kingly duties and no longer needing to disguise herself as a man, and curious about what she would become, Artoria agreed.
Thus, Merlin cast a spell on Artoria, temporarily changing her form to what Shinji sees—transforming from the innocent Saber who didn't understand human hearts, to the perceptive Lantoria who wore less and less.
Incidentally, Artoria's extremely revealing outfit was also Merlin's work—not designed from scratch but modified from Saber-class Artoria's inner garment. That inner garment was naturally fitting on a 150 cm tall girl, but on a 173 cm tall mature woman, it couldn't cover everything. So, Merlin made a few cuts where it couldn't cover, and thus a highly seductive outfit was born. The highly secure, airtight outer armor was also part of this, designed to create a stark contrast and provide the strongest visual impact.
Note: A Servant's battle attire is woven from their magical energy, so there's no need to worry about armor directly rubbing against the skin.
Interestingly, Artoria didn't realize the outfit's impact on men due to her natural innocence in such matters and was quite grateful to Merlin.
Shinji, not hesitating to expose this deception of an innocent maiden, righteously declared, "Merlin is indeed an old pervert; if given the chance, I must give him a good beating."
This righteous stance earned high praise from Artoria, though she had no idea that this master she deemed good had another half of the sentence left unsaid in his heart—"Though I hate to admit it, Merlin, you old pervert, did a splendid job."
For example, what exactly did Shinji do during the Holy Grail War that changed Artoria's fate?
Not much—just a bit of Talk no Justsu, freeing Lancelot, then having Lancelot do some Talk no Justsu, and finally using Gilgamesh's pride to successfully take down this most formidable enemy.
As for why Shinji knew so much about Artoria, he directly attributed it to his master, Scáthach. Although this ageless, immortal queen resides on the world's outskirts, she can observe what happens in the present world, so it's not surprising she knows anything.
However, Shinji didn't deny his efforts. After all, with Scáthach's style, if Shinji didn't ask, she wouldn't interfere with others' fates—except when battle fervor and hot-bloodedness take over.
Then, Artoria inquired about the fate of Shinji's other Servants. During the Holy Grail War, aside from Caster, whom she blasted to death herself, and Assassin, whom she defeated, she hadn't witnessed the deaths of the other Servants and could only rely on speculation.
Shinji didn't hold back and laid everything out.
Lancer Diarmuid died in a fair duel with Scáthach.
Rider Iskandar died in a one-on-one duel with Archer Gilgamesh.
Since Artoria already knew the fates of Archer Gilgamesh and Berserker Lancelot, Shinji detailed that brief yet thrilling battle.
When recounting Lancelot being pierced by multiple Noble Phantasms and still making a desperate final move, his Noble Phantasm, to take Gilgamesh down with him, Artoria's emotions fluctuated violently, nearly losing control.
She admired Lancelot's bravery.
She felt proud of Lancelot's loyalty.
He was still the Knights of the Lake, the First Knight, still the dear friend she knew so well.
Once Artoria calmed down, the two, having known each other for a long time, tacitly avoided mentioning the past and shifted the conversation to the present.
Shinji asked, "Do you have any wishes you want to fulfill, Artoria?"
Artoria shook her head. "No, I have no wishes to entrust to the Holy Grail. This time, I am here merely to fulfill my duty as an observer."
"What duty?"
"To observe this Holy Grail War. This Holy Grail War has many uncertainties, and my task is to determine whether it poses a significant threat to the planet and humanity."
"The planet and humanity—are both Counter Forces paying attention?" Shinji's expression subtly changed. Could it be because of his interference as a transmigrator? The more he thought about it, the more likely it seemed; otherwise, they wouldn't have sent an observer specifically to his side.
"Yes," Artoria nodded. "So, Master—"
"Just call me Shinji."
"Alright, Shinji, I need your help."
"How can I help?"
"I need to gather information on every Master and Servant in this Holy Grail War and observe them. I know it's difficult, but I still hope you can lend me a hand."
Artoria bowed her head solemnly, completely unaware of how enticing this gesture was in her mature form, especially with the pure white expanse of her chest almost spilling out, making one's thoughts wander.
Shinji directed his gaze to the ceiling, avoiding that tempting sight, and softly said, "No need to go through so much trouble. The biggest variable in this Holy Grail War is right in front of you—me."
"You?" Artoria lifted her head, her ahoge swaying.
"Yes. Since you've made a contract with the Counter Force, you should know about the existence of parallel worlds."
"I know a bit," Artoria, though not dead, had become a being similar to a Heroic Spirit due to her contract with the Counter Force.
"This Holy Grail War and the Fuyuki Holy Grail War we participated in are different developments of the same Holy Grail War, in parallel worlds. That means I'm not from this world—I come from another world and have intervened in this Holy Grail War, taking the position of the Black Assassin. The true Black Assassin should have been that child you saw. I think the Counter Force sensed my presence and sent you to observe me."
PS: When Artoria was young, she still had some admiration for Merlin, but the further it went, the more she found him detestable. By the time of "Fate/Grand Order," Artoria looked at Merlin as if he were trash. Tsk tsk.
PS2: Asking for help while exposing what's needed is common sense.
PS3: When people learned about Merlin's existence, they pushed Artoria's ahoge with caution—do you want Merlin watching a live broadcast? Given Merlin's nature, he would keep his eyes on Artoria the whole time. Then it would be, "Hmm, let's tell a story about a king. On a certain day, in a certain month, in a certain small dark room..."