I would be seriously turned off by an RPG with only one character. Having lots of fun characters (and probably shipping them) is one of the main thing I like about RPGs.
But there are novel ways around it. Pokemon is sort of a one-character game. You only play as "the kid", and only one pokemon comes out at a time. Rogue-likes and dungeon crawlers generally have one character at a time, but a lot of characters to choose from. Action RPGs have one character at a time by necessity. I feel like VS Fighting games share a similar character-driven fun with RPGs, and those are one character at a time.
I feel like another way you could keep it interesting is with interesting NPCs. The only game I can think of as an example is Atelier Iris 1. The shop owners are very talkative and involved in the story. I could also imagine a game that's something like a dating sim, where you go on adventures alone and come back to the city to hang out with people.
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As far as working mechanically, there have been a lot of 1v1 RPG and other games out there, so there's plenty of examples to take in. I mean, if you think about the overall strategy, it doesn't really matter that you've got 3 people wailing on 3 monsters or 1 person wailing on 1 monster. A lot of RPGs don't use team combat to its full potential anyways. Like I said, Pokemon, Rogue-likes, Dungeon Crawlers, are all 1 character-at-a-time. You could also borrow some mechanics or philosophies from other types of video games. If I chose my favorites, VS fighting, Racing or Scrolling shooters.
I would recommend that you do skills that do multiple things at once, since you don't have multiple characters to help you out. So like instead of having a spell that cures poison and a spell that heals HP, you could have a spell that heals some HP and removes poison, a spell that heals a lot of hp, and a spell that cures poison and makes a barrier against poison. This would help give your players the feeling that you're giving them something to make up for not having other characters.
Blending in VS Fighting mechanics would be interesting. When people ask me why I like VSF games or what VSF games are like, I say that it's like a game of chess where you have a fraction of a second for each move. I think you could slow down VSF mechanics to RPG speed and still have a strategically interesting game. A lot of VSF has to do with timing. If you use a slow attack that does more damage and stun time, your opponent is more likely to dodge it or block it, or even attack you before your attack connects. But if you do quick attacks that are more likely to hit, the enemy might take a little damage but recover quickly and hit you with something better, or just block the quick attack anyways. Yanfly has the CTB and ATB systems which allow you to use more timing options than the default. Most fighting games also have some form of Rock Paper Scissors, like Strike beats Grab, Grab beats Guard, Guard beats Strike, or High beats Mid beats Low beats High. These work in fighting games because you might see the attack coming and react, or because you get a feel for what the individual opponent likes to do. In completely turn based games, with completely even random odds, there's no point to doing Rock Paper Scissors mechanics.
SumRndmDde has a bunch of Timed Attack plugins that I think could make a 1 character game worth playing.
https://www.youtube.com/watch?v=4Ls2e3nKSVQ&t=248s