To the extent feasible, the entire engine state is saved and loaded. It should cover virtually everything, with the sole exceptions being that linked issue, things like mid-flight network requests that are not possible to save, and things like Drawing Canvas pixels on the basis it's a large amount of data that you may well not want to include. The savegame system should be pretty bulletproof - it's been used widely for many years now, and we've fixed a bunch of bugs over the years.
If something isn't working right, as ever please file an issue so we can fix it. I'd also point out often problems turn out to be mistakes in the project or misunderstandings - if you think the savegame system isn't covering something, prove it! Make a minimal project to test it and file an issue if necessary. I think the state of the feature is better than is portrayed in this thread but I am willing to be proven otherwise with issue reports, which we would then fix to make sure it works reliably.
In my view it really doesn't make sense to tell people not to use a core engine feature and invent their own. Why did we bother making the whole feature if people are going to tell other people not to use it and to make their own? If there is something sub-par about the built-in feature, we should fix it so it does the job its meant to.
Having said that, the savegame feature does include the full state of the gameplay and that can in some cases be a lot of data. The only time I'd agree it's fine to make your own save system is if it's very simple. For example if all you need to save is something like "reached level 5, current score is 120", then the savegame system is probably overkill, and you can just do something like save a small Dictionary with a couple of keys (or your own JSON data). If you want to include all the objects in the layout though, definitely use the built-in savegame feature - there is an absolute ton of stuff to take in to consideration if you want to handle that yourself, but we've already taken care of all that for you.