Let me first tell the situation of Roses. It's the weakest country on the continent. Weakest in military power, in the economy, in almost every aspect. On they side they only have things like "good tourism" but then there is just a little line from the chapter that they come to the country "Horn, one of the Leading TOurist attractions on the continent. Has very low defensive measures". I guess it might sound mundane but let's go back to the Labyrinth.
Why Princess Noel and the Hero of Light were there in the first place? Laberintos, the Labyrinth city is a territory from Roses. If taboo monsters show up, it is Roses business to deal with them, especially right before the resurrection of the Great Demon Lord, everyone is busy, but Noel still is helping. Of course, Sophia being there is a big deal too.
What Leonard sees as "she is always busy" is that she is always running everyone doing desperate diplomatic errands because the country can't deal with most issues by itself. Bending the head, asking favors... imagine a weaker country always asking hep for a stronger country to solve problems they should be able to solve. Roses is in this kind of situation.
That's mostly why as well when all the isekai ppl showed up, they barelly had any priority to chose which one could stay to protect the country. Noel kinda bribed the best ones and the ones that Sophia had to accept, ended up being the wost. I forgot if it is mentioned but 2 of them, one was kicked out because didnt care about fighting, was just fucking maids, and the other one I think got cripled? something, I forgot.
Ok, this is the country state of the situation, back to Sophia herself. This is something that will be revealed in 2 chapters. She was mostly never cruel to Makoto.
Remember how she treated him in Water Temple? It's not that she didn't think he was not worthy, it was because she thought he was too weak to be sent to the frontlines so it was better for him at that point to stay away from combat, because would be safer for such a weak civilian.
Of course, WE knew that he was training insanely and he needed that protection because he needed to farm years of life and yada yada, but that's when comes her defect of judging too fast. Sadly she requires this fast judging of the situation because she just doesn't have time, resources, and time to just slowly access the situation and help everyone. The country can't afford to waste time.
Regarding Leo yes, she looked a bit cruel, but this is mostly her jealousy of Leo lol. At this point to her, Makoto was just one capable fighter that still has his business to take but didn't understand why the Hero of the Country would take lessons from him since mostly Makoto is an Apprentice Magician, and not only that shows how much in a sad state Roses is. The Hero of the Country asking assistance for a simple adventurer of the lowest rank?
Leo argues that its because Makoto's magic is like Art doesn't help because on her head she needs military resources, so she could at least start to deal with the country's issues.
It's not even for pride, this looks bad for the population in general. In the same way, the assistance in Labyrintos, if badly managed, the rumors will make the morale of the country's population drop even more, and if they start to lose the big business ppl from the country, then they are just screwed for good.
That's why even after the Water Temple incident, she still sticks to a harsher approach. Not to be mean, but she needs to show that Roses can hold their shit together and don't need to bend their heads all the time for favors, even if they actually are in a state where they NEED to do that.
And ok, to finish, the icing on the cake, it always looks like she is mean to Makoto because.... of her stare right? The cold stare, emotionless look when saying all of this and making all of this, making then Makoto think that she sees him badly and stuff. That's going to be revealed in chapter 32 (I saw a preview of that), that's when comes into play her skill, "Coldhearted" (forgot the right name). It works really similarly to Makoto's Clearmind, but a weaker version, but the side effect of the person looking like a cold stone wall person is mostly the same. That's why she is always known as an unshakable Princess and doesn't matter how bad the situation of the country is, her knights and civilians still trust her a lot for not losing composure.
So basically her cold stare looks exactly the same as Makoto's from other people's perspectives. More and more it will be clear that when Makoto is fighting desperate situations and is unshaken, ppl start to fear a bit him because he looks like a Psychopath that has no feelings.
TL; DR: The Country is in a sorry poor state that has to beg everyone for assistance for everything. She is the lead of the country and is dealing with issues all the time and needs to stay strong all the time. She mostly never was cruel to Makoto, or she didn't want to throw him to harm, or was just jealous of Leonard. She has a "Coldhearted" skill that makes her outside look like a coldhearted person.