In terms of wide-ranging classification, I am unsure of any that exist. There has been a few attempts in the past (for an example, see John Kim’s System Design series), but always what occurs is that someone ends up describing the mechanics from the perspectives of their own play culture, and are usually encoded through the lens of whatever their preferred game is.
There does exist an example outside of tabletop role-playing and adventure games that I have often wondered if our hobby could replicate, that being Building Blocks of Tabletop Game Design: An Encyclopedia of Mechanisms. What this book ends up doing is that it defines a mechanism, describes its use in successful games, and then talks about potential avenues of implementation.
There is, however, a few issues with regards to tabletop role-playing that makes this a tad difficult, in my mind at least. One of which, is that the primary mechanism at the table is so nebulous its often difficult to fully express how important it is over any enacted mechanism in play - that being the “conversation” - the back and forth between the participants at the table negotiating the fictional space. How and why these elements-of-play are often subject to a thing that often gets referred to as techniques. For example, “roll a d20 and get above a 15 to succeed in a dangerous gambit” could be classified as a mechanism, but how and why the table actually decides to classify something as a “dangerous gambit”, grab the dice, and the various rituals and procedures the table has adopted are the techniques, and they probably dominate the actual in-fiction effect much more so than the actual mechanism itself. This causes the discussion of inert rules or mechanisms a bit tricky in role-playing games, because we really only care about the play in-action, and the implementation of any particular rule is so varied.
This aside, we also have quite a large degree of theoretical pursuits as to what the purpose and use of rules and mechanisms even are. We also debate as to how much a mechanism can resolve - not only the scope, in terms of how many or how big of a thing is being resolved, but whether or not the specific resolution is deciding something about the psuedo-physics of the world, something more related to the theming and narrative, something in-between, or something altogether different. This continues on to quite a lot of other domains - when is something being resolved, does the process of enacting a mechanism impart some degree of authority on the parties enacting it, etc.
Tl;dr - trying to classify mechanisms themselves are pretty tricky.
That said, I could always be wrong here. I could be convinced of maybe trying to collect, in a wiki-post here or something else, of examples of mechanisms we can think of from games, but I think I’d only be interested in such an endeavor if others thought it would be useful.
Let me know your thoughts on this, and how one might (if they can, or even should) categorize and enumerate mechanisms.