In that case, maybe having bug fixing be a two-step process (identify, then fix), might be sensible.

I do this frequently. But sometimes identifying and/or fixing takes more than 2 days.

But you hit on a point that seems to come up a lot. When a user story takes longer than the alloted points, I encourage my junior engineers to split it into two bugs. Exactly like what you say... One bug (or issue or story) describing what you did to typify the problem and another with a suggestion for what to do to fix it.

There doesn't seem to be a lot of industry best practice about how to manage this, so we just do whatever seems best to communicate to other teams (and to ourselves later in time after we've forgotten about the bug) what happened and why.

Bug fix times are probably a pareto distribution. The overwhelming majority will be identifiable within a fixed time box, but not all. So in addition to saying "no bug should take more than 2 days" I would add "if the bug takes more than 2 days, you really need to tell someone, something's going on." And one of the things I work VERY HARD to create is a sense of psychological safety so devs know they're not going to lose their bonus if they randomly picked a bug that was much more wicked than anyone thought.