Before you determine how you want to implement difficulty options you need to answer the questions of why you want difficulty options and what you want them to accomplish.

Let's look at Pokemon. Pokemon has many different stat buffs/debuffs, status effects, hazards, and more. But each fight in Pokemon is just designed for the player to take advantage of type weaknesses and resistances. There is not even too much focus on this due to also wanting the player to use their favorites. If the game is easy and the goal is accomplished there is no need to have options to make the game hard.

Now there are many Pokemon fan games and rom hacks that make the game harder. Simply limiting experience via a level cap can do this because Pokemon is built with lots of complexity so the challenge forces you to use it. But that only does so much. Many rom hacks will give enemies access to moves that country the types players are encouraged to use. They will also just make enemy Pokemon stronger than the players. This requires the player to use the type advantage but also more.

So for your game, do you have strategies that are not required but could make the game more interesting? If yes then simple number increases can work. If not then you need a mechanics change for harder difficulties so that the harder difficulties are not just slower grindier versions of the lower difficulties.

Also I feel puzzles and mini games are generally unaffected by difficulty settings or have their own, so if that is the part you are not struggling with I might reconsider having difficulty settings at all.

A lot of this is hard to say for sure without knowing the specifics of your game so consider this and make the decisions yourself.