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Most topology problems fall into well-known patterns; there aren't too many to become familiar with. …

Edit (Better understanding of OP) If you show the internal triangulation for rendering by using a Wireframe node, you can see that the (non-planar) quads are indeed triangulated in opposite directions …

AltE > Extrude Manifold should clean this up automatically, in the extrude operation itself. (Blender 2.9+)

This may be a naive answer, I'm no coder, but is there anything wrong with letting BMLoop.is_convex do this for you? (Starting from Edit Mode): import bpy import bmesh obj = bpy.context.edit_object m …

Assuming your Bevels are set by a Bevel modifier, not hard-wired, this is a Snap. In this example, Snap is set to 'To: Vertex', and 'With: Active', and to influence 'Scale'. The Transform Orientation …

If you were taking a sub-d approach, I don't see anything in this particular model which requires tricky transitions from high-density to low-density mesh, especially if you can model separate parts a …

If you're working with subdivision, something like this is all you need: As you can see, you can loosen or tighten the curve by bringing internal holding edges closer to, or further from, the corne …

@batFINGER's or something like it, is clearly the most accurate way, but if eyeballing is enough, you can use the Spin tool to create an arc between 3 points. If the 2 end vertices are not aligned to …

This kind of topology is most often the result of automation; Booleans. where the intersection between surfaces is programatically calculated, or automatic conversion from other data-formats. … If modelling by hand, the topology does not play well with polygonal modelling systems, including Blender, that are geared to the selection and manipulation of loops and rings of edges bounding 'tracks …

A quick way to fix your topology: Starting with the wrong number of vertices, having X > deleted faces only Select the square's edges, and WSsubdivide with 7 cuts Select both edge loops, and CtrlE … By far the most common because of the shown topology - comes naturally out of a quad, the diagonals can be absorbed in 5-poles in a holding loop around the circle, or your beveled edges, so don't propagate …

An approach using Bridge Edge Loops.. this may or may not be the style of fillet you're looking for, but the tool gives a lot of flexibility. .. arrange isolating face rings either side of the junc …

The quickest method I've found, which doesn't outwit Booleans, fills, or intersection-finding... Starting in the flat, with your collection of edges filled or not, Mesh menu > Knife Project them down …

As @Gordon has noted, all-quads are probably not necessary on a flat, rigid surface. After a level of Subdiv. the faces will be quads anyway. But that means.. .. subdividing once can often offer a so …

I think the main factor is the topology. …

If at all possible, I would work the other way round, without the circular topo.. It's easier to make a square region circular, than to make a quarter-circle square. Grid Inset squares (you could ma …