You could use Fate. Fate is a generic system that can do high fantasy just fine. It doesn't need a full party like D&D does. It handles social and physical conflict equally well. The way aspects work is very "As long as I can justify it in the story, it could happen". You can spend fate points as a player to alter the story, too, which is fun. I also like that it's generally "You can get what you want, if you're lucky or pay the price". "Succeed at a major cost" is almost always on the table.

The downside is it has big "tyranny of the blank page". D&D-likes you can just point at "Human Fighter" and go. Fate asks you to come up with your high concept, trouble, and background on your own. If you're creative and that excites you, it's freeing and exhilarating. If you're shy, it can be overwhelming.

The core rules don't have a detailed magic system. It's up to you to decide how you want it to work, or to buy a splatbook where someone else made a system. It's pretty easy to tinker with.

It's also up to the GM to make sure the threats are reasonable. There's no "CR" system like D&D. But players also always have the power to concede, where they lose the immediate conflict but survive. You don't have to worry about accidentally wiping the player(s) usually.

You could look for some PbtA games, which are extremely popular. I personally don't like them much because playbooks feel more like mad libs than creative writing. I also don't like the dice system, and often find it punishing to the point of not being fun. (I just played a PbtA game last night and don't think I rolled even a success on like 6 rolls in a row. I felt incompetent and it sucked).

I know that Ironsworn is decent for this sort of thing, as that's singleplayer and single GM capable. I'm not sure if it's high fantasy, though. I think you could also do something with any old D&D game up to 3.5e if you change up the rules a bit to ensure it becomes single player and single DM capable, but I'd have to take a look at how people could do this.

I have really enjoyed Maze Rats for this sort of thing. It's a very minimal OSR system, but gives enough structure that a dialogue between one player and one GM is really easy and natural in the framework of the game. Negotiating for spell effects also allows a bit of lawyering that isn't per se about rules, if you like.

my SO and I have had a lot of fun with Scarlet Heroes.

Dungeon Dive keeps telling me that Scarlet Heroes + Whitebox is a great solo experience (or one player and one GM) you can replace Whitebox with your preferred OSR theme setting.

I think Godbound could be a really interesting system for a one on one. Players take on the role of literal gods, and are forces to be reckoned with even at first level. And their godly powers are really game breaking, but totally on purpose! In fact, one condition of passing to level 2 is to have changed the world around you. This is done through some super nifty systems that let you (the GM) handle villages, factions and so on with very few stats. Like all books by Kevin Crawford, itvs designed for sandbox style adventures and comes with practical tips on how to prepare yourself to handle things without burning yourself out.

It's an OSR game, but Godbound feels particularly narrativist, to me. For example no skills, just a d20 roll under your stat, if at all needed. And you get a +4 bonus if any of your Facts (think, Aspects in Fate) apply. I won't go into combat details, but to put it succinctly : you don't even look at the Hit Points of your enemies, you do damage in Hit Dice! So even the most peaceful of PCs can wipe the floor without even making an effort. Think the Three Kingdoms video games, where your hero can take on entire battalion as a matter of course (and yes there are rules for that, and yes, they are simple)

And there are two adventures set in the China inspired area of the setting, to really get the idea that this more wuxia than sword and sorcery. If you know Exalted? That's the version with rules that won't drive you mad with all the bean counting.

Scarlet Heroes mentioned elsewhere is by the same author. An Echo Resounding is an extension for it. Combined, they are an earlier incarnation of Godbound, in my opinion. In the sense that all the stuff you find in those two books got refined and unified in Godbound. And then pushed to eleven because now you play freaking gods (and there are optional rules to play mortals).