I have been thinking a bit about these 2 posts, since they are the only ones that tried to answer the question of 'complexity' and 'depth'. The links in the quotes below are direct links to the posts I am referencing.
I think the main thing that stands out to between the 2 post is that you both seem to have differing ideas about what complexity and depth actually are. With Quuoooote saying mechanical depth is part of complexity and Shurrikhan saying complexity is real decision making, which can be seen as part of the cognitive load, which is described as Depth. Now granted, these are very simplistic oversimplifications to what was said, but that was one of the first things that stuck out at me.
Even looking at the posts deeper Quuoooote describes depth as how different mechanics interact with each other and cause friction, whereas Shurrikhan describes a similar concept, but calls it complexity.
Can you see how these sorts of discussions go nowhere when, even between 2 people, the discussion about what makes a job complex and what adds depth, whilst related, are different.
It also bugs me that a simple, objective description wasn't given. They are either described as 'look here, that is depth' or talking about cognitive load, which is a purely subjective stance. If I find one job easy to play, but someone else really struggles to play it, If I want the job to be more complex/have more depth, that is fine, but the other person says no, it is fine where it is. Both are valid points, but neither are helpful in the discussion as to what makes a job complex/deep.
If you were to ask me, I would answer the following:
Job Depth
The amount of mechanics a job has to juggle.
In the case of Bard, this is keeping track of DoTs, keeping up the song rotation, keeping on top of Repertoire procs, etc. In effect, this is purely a list of the mechanics on the job. If better fight design/job changes also allow it, this could include things like a non rotational gap closer/widener etc.
Job Complexity
This describes how the mechanics listed above interact with each other and fit together.
This is then when you get things like having 2 GCDs fighting for the same spot, so you have to make a decision, or Army's Paeon messing with your GCD speed so that Empyreal Arrow timing gets messed up, this would have been how the DoTs interact with the songs to get Repertoire procs etc. This how they both complement ach other, and create points of friction.
In my opinion, these are much better descriptors as they are objective in their meaning, there is no arguing based on how someone feels about something. However, I think the biggest thing here is that they are easy to understand. If we want to have productive conversations about these sorts of things, we don't want to bog people down with overly complex terminology if we can help it.