Guardian Recall (ガーディアンリコール 〜守護獣召喚〜), released 10/1/1998, developed by Agmix, published by Xing

This game was originally released for PC98 in 1996 as an eroge; the Playstation port is a complete (all ages) remake. I don’t know all the details of the original game but it sounds like both the battle system and the story were extensively redone.
The basic premise of the game is that all the characters can summon Guardian Beasts that actually fight for them (it’s basically Stands from Jojo). You can directly control your human people, but they can’t directly attack. All the attacking has to be done by the Guardians, who can only be controlled by AI settings. The AI system has more care put into it than some of the other AI-based games I’ve played, but in the end I think I just prefer to control my characters.
All of the main characters and non-grunt enemies are female, with no in-world reasoning (they don’t even try to explain it, I guess when it’s an eroge nobody cares).
The game takes place over 40 stages in 5 chapters. The first two chapters are parallel in time and can be played in either order, but after that you play the other 3 sequentially.

Each character has three main point pools, which they share with their guardian. SP is hit points. MP is used to issue commands to the guardians — when it reaches 0, you lose control over the guardian and it starts attacking randomly (I think you can still recall it though even when it does this). AP is for the spells that the human characters can use.

You choose your AI command from a list, that grows as you level up. The number is the amount of MP it uses per turn (which is increased if the guardian is far away from the human). The AI command not only affects how the guardian will act, but also will shift the stats of the guardian. The basic AI command is “protect me”, which will cause the guardian to stay near the human and only attack nearby units. Some of the other commands are “attack!” (which will send them out), “heal”, “move to a specific point”, and “don’t do anything.”
So you can’t guarantee that your guardian will do exactly what you want, but you can shift it to make it more likely. There is also a tendency for guardians to attack each other rather than going for the humans, although they will go for the humans in some cases.

The guardians have an elemental (of 8), and there is the standard compatibility chart between elements. They also have ranks in various types of attacks, starting with D (which means they can’t do it at all) up to S. The numbers after the rank show how the guardian will develop when they rank up (so in the picture above, Pochi is probably going to be Short S, Long C or maybe B, and Heal C at the next rank up). They also get some special abilities that activate in certain cases.

The game works on a typical player/enemy turn system. Each turn, each human character can do three things in any order — move, change AI setting, and either use an item or a spell. The guardian will act when you end your turn (or if you choose “carry out order” in the AI menu).
There are hidden items on the map (I don’t know why this is such a common thing in SRPGs, who decided this was a good game element?) You can also get a lot of bonus items from using the “talk” ability, either between your own characters or between you and the enemies. The ones where you have to talk to the enemies are often quite difficult to get because you have to maneuver your humans to the other humans without getting killed (or without killing the enemy), which can be tricky. I’ve found it not very worth it, although if the game gets harder later I might regret not getting more items.

Most of the dialogue is not voiced, but there are a fair number of anime sequences, some of which are rather long.
So far I have only played the first two chapters (16 stages). The story doesn’t develop a whole lot in this segment, it mostly just introduces the characters and the basic situation. The enemy group, called Egubado, is trying to cause chaos and possibly destroy Japan. I believe that they were the cause of a big earthquake in 1999 (this takes place in 2017 or so). Seven of the girls on your team were all born in 1999 and they get called by the Dragon Spirits — currently our goal is just to find all the dwelling places of those spirits and awaken them.

So I have 24 more stages.
One other issue with this game that gets brought up a lot is that it’s rather slow. You can fortunately turn off animations but even so it takes a long time for everything to happen, and load times are long. Duckstation is efficient enough that I can get a good emulator speedup, so it’s not as bad as it would be on a real console (this is why my rating system is unfair to Saturn games, but that’s another issue….)