There are free engines available, and many of the paid ones have cheap or free tiers available for smaller projects. Also, if you want to actually publish your mod, there are likely to be a bunch of costs, like buying licences to use copyrighted characters, settings, ect. Even more so if you want to publish your mod as a standalone product, where you need to buy a licence to resell the entire original game.

That said, prehaps it would help to think of the game engine as a foundation, and the games as a completed house. If you want to make something, you can look at existing houses and imagine putting an extention on, or a new coat of paint. If the house is particularly well contructed, maybe its even easy to do. Still, at a certain point, theres no more you can add or change without it being easier to tear everything down and start from the foundation, or entirely from scratch. Its not a limitation of the design of the house, its just an intrinsic fact when you’re working by building off someone else’s completed work.

Now, if we start from the foundation (engine) instead we have less to start with, meaning its going to be a lot more work than doing minor changes, but the hardest part is still already done for us. This is what most people do when making games. Its far more flexable than modding, esspecially because you have a selection of engines available at different prices, with different strengths, weaknesses and specializations. GameMaker for simple 2D games, RPGMaker for making jrpgs, Unreal for 3D action games, ect.

Finally, you could skip both these options, and design and build everything from scatch. Its the option that gives you most freedom by far, but its generally not worth it unless you’re making something thats very small, that is so unique that nothing else will work, or that you’re dedicated and what a perfect fit for.