I was thinking about making a solo battle project to go with a combo system I was considering. I like the idea of being able to take bonus actions or chain extra attacks for playing smart, but a system like that could make battles a drag if you had to take long turns for each party member. It would be tough to balance, but I think you could replicate the feeling of having a party by giving a single character multiple actions and then giving the player multiple goals to juggle.
* Enemy Phases: I think this might be necessary to prevent battles from being just the player and enemy smacking each other until the one with the biggest numbers is left standing. You could give the enemies a pattern where they rotate actions (charge up -> attack -> defend) so the player needs to counter their strategy (attack -> defend -> charge up). Another method would be to give bigger enemies multiple health bars and have different effects applied in each phase (1st bar - enemy's attacks inflict poison, 2nd bar - enemy's attacks reduce player's healing).
* Conflicting Goals: Players should have more things they want to do than they have actions. Maybe require the player to use one type of attack to build up critical hits, but a different type of attack to build up limit breaks. Make highly desired effects (healing, debuff removal, evasion, limit breaks) require some effort to use instead of being on-demand at all times through a skill. If the player has to be proactive in order to make sure a necessary ability is available when they need it, then it should help keep the player more engaged as they consider what to build up and when.
* Break Status: Battles shouldn't drag out in any battle system, but when the player only has 1 character to use then it would probably be good to give them a way to end fights quickly if they make the right moves. A way to break the enemy's defenses and let the player hammer away at them for a bit could be a satisfying way to handle normal enemies. This should require a little work by the player to set up. Maybe make weaker enemies get stunned after a limit break and lose a turn or two, which gives players time to try and charge their limit break back up to keep them stun-locked.
* Communication: I recommend this for every game, but use the UI to make the player aware of what they need to play around. Show the enemy's limit meter so the player can plan to have a defense ready for when it is charged. Give the enemy a scary red aura when a health bar gets broken so players know to expect more aggressive attacks. Show enemy buffs/debuffs so the player can see what effects are in play, like if the enemy goes reckless and raises its attack while lowering its defense.
You might be able to do this in a 1 action per turn system, but I think either a way to chain multiple attacks per turn or a way to gain extra turns might be better to keep things interesting. You can still keep things balanced by making powerful actions take the player's full turn, or delay their next turn. And you can always prevent the player from combining different types of actions, like preventing them from using selecting "Item" as their second action if they attacked on their first.
When in doubt, check out other games that are 1v1 (like card games or action games) to see what they do. There's nothing wrong with borrowing ideas you like from other games if you think it will make your game better.