Shin Megami Tensei III, get it now. (I just ordered a copy for myself physical PS4 for €16) This cuts a lot story bullshit, and focuses on exploration and combat. You can play around with your demons, and customize a decent amount. You're a nordic, too so I don't know if you can pick up cheap stuff from Sweden. Look up prisjakt.nu, or pricerunner.se
Shin Megami Tensei V might not be as good, but it is still a high quality game, with some performance issues, though.
Most of the SaGa games. I would advise you to try either
Romancing SaGa: Minstrel Song,
Romacing SaGa 3, or
SaGa Frontier as your first entry. While I adore SaGa: Scarlet Grace, and Romacing SaGa 2, I do not feel confident enough to recommend them as first foray into the series. The games use learn-by-doing systems, and when you use a weapon, you will eventually "spark" attacks for that weapon. The games lets you choose a starting main character, and this can determine what party members you get, what scenarios you can see, and more. They usually have banger soundtracks, and the writing is functional. What has kept this series so good, is that the creator is still around, and caring for it. Kawazu is behind great games. The games are very obtuse, but feel so rewarding once you figure things out.
The Last Remnant, also headed by Kawazu. It is SaGa in all but nmae. While it does have some of the anime stuff you might hate, the game is so unique, that I can't really find anything like it. You don't use characters per se in combat. You do recruit characters, and all that, but you use unions. Mix characters to create good unions. Some good at healing, some at melee, some at range, and so on. I loved this game back in the day, and replayed on PC not very long ago. I still liked it. Just as the SaGa series, it can be very obtuse in its system. This one is even more rewarding once you figure things out. I remember at the start, that I was disappointed, but 94 hours later, with the super secret bosses, and the overpowered version of the final boss defeated, I was very happy.
Dungeon Encounters. It may seems so simple in its execution, and at the start, you might think to yourself, is that all there is to this? But the game gives you more and more options as you go. Lose a party? If you have a reserve party at your base, time to go on a rescue mission, but you can't grab a full party for rescuing people, there needs to be open slots. Want to try to skip some of the 100 flors? If you have the right teleportation spell, be my guest. But, but, but, but! You might end up in hell, or who knows where in the game world. Time to search for your lost party. The game uses an armor system like in Original Sin 2, which I was critical of, but here it isn't as annoying.
Tale of Wuxia: Pre-Sequel is a very solid Chinese rpg, with a terribad translation (but it does produce some gems as shown below). But I liked everything else so much, that I just went with it. It lets you recruit a fair amount of party members, has turn-based combat, and a world map. You travel on it to go to new places, but it is not a jrpg style world map, it's an overview map.
Ho Tu Lo Shu. This only has a fan translation, or if one can even call it that. It's machine translation, with some edits here and there. Made by the Tale of Wuxia Studio. While the translation is more miss than hit, it is still one of my favorite rpgs in recent memory. Fun combat, exploration, and lots of characters to choose from as party members. You have the possibility to customize a lot when it comes to your characters abilities and more.
Bravely Default 2. It has pretty bad graphics, and not such a good soundtrack compared to other games in the series, but it is still fun because it offers a lot more jobs than Octopath Traveler 2, and some fight in the latter stages are very fun. Octo and BD series are both headed by Asano. I think that there is a Switch demo, if they did not remove it. (I checked, demo is still there.)
Triangle Strategy is a very divisive game, also headed by Asano. Very dialog heavy, and you don't get to customize your characters as much as other trpgs. Only try demo before considering this.
Octopath Traveler II. I you think the first game is decent, the second game is the same thing with some slight improvements here and there. Looks even better than the first game, has some fun secret bosses, and has a great soundtrack. Has a demo.
Front Mission 1 and 2. If you're interested in trying mech tactical rpgs, go for these ones. These are less anime, and more serious in tone. The second game's port seemed to be less than stellar at release, but it was its first official English release. While the mech customization isn't amazingly deep, you can still mess around with different combinations.
There's
Brigandine: Legends of Runersia, but your mileage might vary on this one. I'll let someone else describe it further. A bit on the easy side, but
Undernauts: Labyrinth of Yomi is a blobber with an unusal setting. I would like to recommend you
Star Ocean: The Second Story R, but I have my doubts about you liking it. I know there is a Switch demo.
Baten Kaitos I and II. These are a bit different and use a card system for its battles. It can take some time getting used to.