Three are common, three are uncommon.
The work on this has already been done for spells, as you linked in your question, and from looking over the various monster manuals, the pattern seems to hold pretty well. Dex, Wis, and Con saves are wildly more common than the other three, by something like to 4-to-1.
Among those, Constitution is probably the most-used save due to the number of venomous monsters out there, and I feel justified in calling out Intelligence as the least used save overall.
But that's not nearly the whole story. Some abilities call for a save from a single target, while others affect everyone in an area, so while you could call that "one dex-based spell/ability and one con-based spell/ability", they're not really going to have the same amount of impact at the table. A single dragon or fireball may be responsible for a half-dozen Dex saves at a time, while a whole group of snakes might only inflict two or three hits that require Con saves. Furthermore, some spells and creatures show up often in games, depending on the game (like, say, dragons), while others are often going to show up only one time if at all (like an astral dreadnought). Should those creatures be counted the same way?
Ultimately, which saves show up most often at the table is going to depend heavily on choices your DM makes rather than raw counts of "How many things can I find in a book that call for this save?" Even then, not all saving throws are equal -- Strength saves are often made to avoid relatively minor inconveniences like getting pushed back or knocked down, while a failed Wisdom or Intelligence save is often incapacitating.
Does "most" and "least" really matter?
The best analysis here is a higher-level view. It's not about exact counts of effects or trying to determine how often they're each going to show up on your particular table; rather it's the general understanding that Con, Dex, and Wis are common saves, while bonuses to Int, Cha, and Str are not very often used.
Which of the three "important" saves is "most important"? It depends on your game, your DM, your party, and other elements. Which of the others is "least" important? Well, Intelligence, really, but none of them are particularly common, so it's hard to just pick out one and say "this one is the worst". Generally, failing a saving throw sucks no matter which save it was, so it's more just picking your poison.
