Well, it depends on how you want to do it. You have the right idea with storing the scene, you just likely will need to do additional processing to get the player (and potentially other entities) into the correct position after loading.
If you are okay with the idea of fixed save points, then I would have each level have a dictionary of save points and then store the scene and the key/name of the fixed save point. Then, when loading, you can spawn the player, find the correct spawn point using the saved key/name, and then move the player into position. To do this, I generally have a "spawn point manager" class that, when the scene is loaded, is passed information on where to spawn the player, and what data to use (generally from an autoload script). I've done this before for a few games and it works decently, though it has some limitations. The biggest limitation is that it forces the player to save at specified points, they will not be able to just save anywhere.
If you want to allow the player to save anywhere in the scene, without a specific save point, then you will need to store the global position of the player, along with which scene they are in. Then, when loading, you can spawn the player and manually set the position to the stored global position in the save file. Just keep in mind, with this situation, you will likely need to make some minor limitations in where and when the player can save, so the player cannot save during transitions, cut-scenes/cinematics/in-battle, etc. If you want other entities to be in the same position, like NPC characters, you will need to store their positions (and any relevant data) as well, and on load spawn/move them in the correct positions. The biggest limitation with this method is just getting it working right and fixing the little limitations that pop up as you progress. I personally have not employed this method in any of my projects, but I know from other experience it is a fairly common approach.
All in all, it really just depends on how you want to do it. I would suggest implementing whatever seems like the best for you and/or what you know how to implement. While overhauling the save/load system later in development can be tricky, the difference between fixed-save points and the ability to save anywhere is mostly just how the data is stored and how the player (and other entities) are spawned, so in theory it should be possible to swap them out later in development if needed.
Hopefully this helps a bit! :smile: