Whoops, my bad for assuming you're up to date.
In terms of actual pitching style, Kataoka and Sawamura are very different. One is a power pitcher with a Curveball while the other is a finese South Paw with moving pitches. However, the similarities between them are numerous. They are both the hardest worker within their team, Sawamura is always the last guy on running on the ground, pulling a tire and Kataoka was the same. They weren't exactly repsected by their teammates when they first came up, they have to slowly gain that trust through time with their performance. Furuya on the other hand was impressive out of the gate and people has high expectations for him. So yes, the similarities are there and you could say it did more or less played a certain part in why Kataoka choose to go with Sawamura for Summer.
I'll response to both of your last points together as they're related. The more accurate description to this would be that yes Kataoka does trust Sawamura but it wasn't as much as he trusted Furuya, because the later was the Ace of the team. Furuya had a meteoric rise to the top, he has a fastball velocity that's unrivaled in high school, he performed well when Sawamura and Kawakami were still very shaken after losing to Inajitsu. At that point, there's no reason for Kataoka or Miyuki to expect Sawamura would become the Ace especially in high school setting where the Ace jersey hardly ever change ownership once a guy possesses it. Now this leads into the Yakushi game. Technically, there was really no need to make a pitcher switch because frankly the last 3 guys up were the guys at the bottom of the lineup (aka the worst batters on lineup) and Sawamura just went through the heart of Yakushi lineup striking out their best 2 batters, Raichi and Sanada; he could handled the cleanups, he could have easily handled the last 3 guys. Both Raichi and Sanada got struckout despite having seen Sawamura's pitches 2 times through the order, the 3 guys on the bottom of Yakushi llineup weren't going to do better. Considering that momentum Sawamura had, on top of Seidou coming back on the top of the inning (which has already landed a huge blow to Yakushi's confidence) and the fact that Furuya was injured, there really was no need to make a pitcher switch. However, ultimately what was coming into play here is to Kataoka, going with the Ace for this situation shows that he trusts the guy and you're supposed to trust your Ace regardless of what his condition is, either he's injured or he just had a bad game, when the title is at stake, you go with the guy you trust most, even if you lose you suck it up to that decision. It was a controversal decision but there were sensible reasons behind it. On the other hand, it was clearly a narrative choice that set up Act 2 by Terajima, that unless you're actually the Ace of the team, when push comes to shove, it's difficult for the coach to favor you over the Ace, it is how it is so if you don't like it, become the Ace. To me, the tactical choice due to mental advantage or whatever was less signficant to the importance of Kataoka going with his Ace, the pitcher he trusts and that was sort of a microcosm of the entire Act 1.
Now back to the point of Miyuki and Kataoka actually believes Sawamura can become the Ace or not, to me it really didn't occur to them that Sawamura can actually be the Ace until the Spring Tournament. Kataoka's decision in Act 1 is an evidence that although Kataoka does trust Sawamura but that trust is only limited to certain extent, he's not willing to give Sawamura the benefit of the doubt that even when the guy is struggling, he's willing to give him a 2nd a 3rd chance to prove himself like what he gave Furuya in the Ichidaisan game and regardless of the validity of said decision, you can sort of see why he did such a thing because he knew Furuya was capable of greatness that he's shown in the Sebatsu. Kataoka just didn't expect his Ace to be that inconsistent and at the same time, him apologizing to Sawamura in that same game is a clear indication how much he was willing to give his Ace more leeway, so much so that he threw away the game and injured the guys waiting in line to save the game, Sawamura. From the narrative Miyuki and Kataoka does sort of expect Sawamura to become good but because Furuya is the Ace and he's shown good stuffs at times that it's difficult for them to dare think that they have another great pitcher in the same team but the fact that Sawamura surprised them and made them having to change their expectation for him in Act 2 is real. They were definitely surprised and they had to reconstruct how they were going to view Sawamura as a potential candidate in Act 2, before that in Fall, there was no reason for them to think otherwise. To have 2 pitchers equally as good as one another in the same year rarely ever happens so we could see how such a situation could surprise everyone involved and not just Miyuki and Kataoka.
Yeah, you'll see it later but Kataoka's former mentor, Sasaki has a great quote: "It's the team that nurture the Ace and it's the Ace that makes the team strong". It's a multual relationship that fortify both the team and the Ace and I think that's the way Terajima is going to navigate through the remaining of Act 2.