Hi! Sorry for taking so long to answer this. I was holding off on this because I've literally spent days wracking my brain trying to come up with something more substantial, but couldn't really, so I'm just gonna share what I have and say that if anyone reading this has their own suggestions, sound off in the comments!
Anyway, I'll say up front that I personally don't quite put Sakura Taisen games in the dating sim bucket when thinking about its overall place in the 90s console galge gold rush. It's absolutely responding to games like Tokimeki Memorial for sure and almost certainly either wouldn't exist or at least not in its final state were it not for Konami's success. But for a handful of somewhat nitpicky reasons I'll mostly spare you and everybody else reading this except for this footnote I'll leave right here1, I mostly just consider it part of the wider galge milieu of that time.
If I were to describe it more in more specific terms, what I would say it has a lot more directly in common and is most interested in iterating upon is Japanese PC adventure games, particularly ones earlier in the 90s for the PC-98. There's a lot of very specific presentational and structural tricks and flourishes that Sega/Red Company took pretty much whole hog from that playbook that are immediately recognizable as descending from that school of design once you've studied enough of those games. As I've sometimes semi-joked online and with friends, Sega was perhaps the best PC-98 developer that never was (especially when it comes to Sakura Taisen 2, which is a master class on that style of game as it was on its last legs in the mainstream Japanese industry). And indeed, there were plenty of other games on that platform that melded SRPG gameplay with traditional Japanese adventure game storytelling between missions, so it's ultimately a game with plenty of precedent in its own right; just a lot less so at the time within the console space specifically.
None of that prevents me from answering your question, of course, because Sakura Taisen itself left its own lingering mark in the space. If Tokimeki Memorial's success showed that character raising and PC-style galge could have a place within the console industry—because it's important to stress, before then, even in Japan among that audience, those games were routinely written off as indulgent fluff for lonely otaku—as another game from one of the pillars of the industry, Sakura Taisen proved that this wasn't merely a one-off, flash in the pan moment; if you were a big, more traditional developer or publisher and you wanted to make a move in that space, you could absolutely thrive, and in Sakura Taisen's case, it had cross-media staying power that lasted well over a decade, persisting even years after the last numbered installment of the original line.
What makes this question a little tricky for me to answer in the moment is that, unless I'm missing more obvious examples (and it's entirely possible I am, I haven't been running on a ton of sleep lately), I would say that post-Sakura Taisen games generally tended to learn from it more in terms of broader structural strokes (eg: the balance between narrative/relationship building moments vs. "actual" gameplay, etc.) and that merchandising end, rather than merely attempting to mimic it, which was probably the right call because at the end of the day, those original Sakura Taisen games are the product of a group of creators with very specific skills, professional experience, and, again, influences that would be really hard for most any other developer to replicate. And as of we've seen a couple of times now, even Sega has struggled to make lightning strike again for that series post-4; 5 isn't exactly as widely beloved as the previous games with the actual series' namesake and "Shin," the most recent one that finally did get a localization from Sega proper ultimately came and went, if maybe a little bit more successfully, I would reckon, albeit not enough for their tastes.
Regardless, for people like you who want a recognizably Sakura Taisen-adjacent experience in a different package, I think the go-to recommendation is probably the Galaxy Angel series for PS2/PC. There are six of these in total split across two separate trilogies, each with their own cast of characters. It's not without its differences, especially in terms of combat mechanics, which I would basically describe as being a simplified space combat RTS (and it rules), but that ebb and flow of "story>mission>social time, rinse, lather and repeat" makes it abundantly clear what series developer Broccoli looked up to while creating it. I haven't played all of them (only all of the first one and some of 2; one of these days I'll finish at least the whole trilogy), so I can't speak with all that much authority on these games compared to, say, good friend of the feed @Kimimi, but they're absolutely charming games for what they are. Lower rent and scrappier in just about every way compared to Sakura Taisen (don't expect that series' production values by any means), but they make for good comfort food when you want another game that more than competently executes on a lot of those same basic ideas while still being plenty enjoyable on its own merits. To my knowledge, that original trilogy has been fan translated on PC, but I can't vouch for the quality of the English, especially given that those patches are real, real old. If possible, my recommendation to anyone reading this would be to stick to the PS2 games; not only is it entirely possible that Galaxy Angel has compatibility headaches under modern Windows, but from what little I've played of that PC version on an appropriately specced PC that I have, I just think the combat in particular controls better on console, believe it or not.
Anyway, like I mentioned, if people have other recommendations for analogous experiences, definitely sound off in the comments below! I feel like I'm missing something else that should be obvious to me and it's driving me absolutely bonkers! (Googling in Japanese suggests that some people see the Summon Night series as scratching a similar itch, which I believe I've also heard from English-speaking players, for what it's worth, though.) For my money, I would really recommend exploring older Japanese PC adventure games (insofar as you're, y'know, comfortable with potentially adult subject matter in a decent amount of those games) and Red Entertainment's games. From what I'm aware, they've historically handled more conceptual and overarching design stuff rather than getting their hands dirty with nitty-gritty development specifically, but if you look at the trajectory of their games leading to their collaboration with Sega on Sakura Taisen and who they'd been working with up until that point, you can see a pretty clear through line for how they ultimately got there.
I wish I had more than just a single series to offer specifically, but hopefully that's at least a decent starting point! Thanks for the great question! 
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The main reason I tend not to count Sakura Taisen as a dating sim per se is because while the relationship building is obviously important and pays off in the combat, the systems themselves are pretty basic and don't really offer much in the way of player flexibility or route planning in the way that something like Tokimeki Memorial offers. Which is to say, while the stats and scheduling systems in Tokimeki Memorial afford you a lot of latitude in terms of how you achieve your set goals, with Sakura Taisen, it's mostly whether you trigger a set of flags for each individual girl by certain story specific deadlines. The LIPS system is neat enough, but even in its more fleshed out incarnations in later games, it can only offer so much impactful variety that informs your decision making as a player, you know? Basically, its relationship systems aren't simulation-style in nature and that's why I don't consider it a dating sim in the strictest sense, even if I obviously still otherwise like the older games quite a bit!
