these are remanents of the way ryuseitai used to refer to each other in the early stories (particularly 2015-2016), and so you'll likely find them in the very old story fan translations or in old physically released content (like the first ryuseitai CD drama from 2015). it's not just shinkai-san, there was also:

• shinobu used to call midori "takamine-dono" (was in hero show and the drama CD)
• tetora used to sometimes call chiaki "leader" instead of "taichou" (bits of this still exists in ! era main story, and drama CD)
• tetora used to call shinobu "shinobu-kun" from as early as piratefes, a story set in summer
• midori used to call chiaki "taichou" in hero show and drama CD, "buchou" in 2015 sportsfes
• shinkai-san used to be in hero show too
• there were likely more so this is just a rough list

it seems that eventually, enstars finally settled on how they want each ryuseitai member to refer to each other, so a lot of the stories got their namings adjusted in-game after months of their release. now in-game, hero show has shinobu say "midori-kun", all of tetora's "shinobu-kun"'s that chronologically happen before repayment festival were changed to "sengoku-kun" since that's when tetora consciously makes an effort to switch namings, and so on and so forth.

but again, there's still some small remains of the initial namings not just in old fan translations, like the physically released drama CD from 2015, or the first main story of ! era.

as for why the characters used to call each other with those names at first, i'm not sure because i came to the fandom in late 2016 🤔 i guess they felt like it worked at the time enstars was released, but as the characters got more depth and shape, they decided it'd make more sense to settle on certain other namings.

i can see why they'd change takamine-dono for example, because it is strange that shinobu would call midori that when he calls tetora "tetora-kun" (and eventually it's established in sparkly first years that shinobu and midori got along as early as they first joined school, so "midori-kun" definitely fits a lot more). and although "shinkai-san" is polite and suits tetora's respectful way of speaking, it sounds more distant than "shinkai-senpai" (which more clearly refers to him as a senpai from the same school).

for midori, maybe they figured it'd make most sense that he doesn't keep switching between "taichou", "buchou", and "morisawa-senpai" all depending on where he is with chiaki (unit, club, or any other situation), and made him settle with morisawa-senpai. on that note, hero show has a moment where midori calls him "buchou", and then chiaki tells him to call him "taichou" when they're doing unit activities, not "buchou"... so i like to imagine midori got tired of constantly needing to switch depending on the place and went for something easier. but this is completely speculation!! most of these namings got silently changed so we're prooobably meant to see most of it as "that was how they were always referring to each other from the beginning" LOL