My eyes must have glazed over in my first reading, when you brought up you had "many other cutting tools for landscaping that can share the sharpening tools". Mebbe it was just the shock value of the statement that made me look away.
Then, in Post #4, you talked about new pruners and lopers.
Sharing sharpening tools between culinary knives and landscaping cutlery? I have to really hesitate on that one.
Let's look at each separately. To do so, it helps to bring three words into the dialogue: "toughness", "brittleness" and "hardness".
All three words are relative. They are not absolute, but instead are comparative words. And we use all three of the words when comparing steels, knives and tools.
Toughness and brittleness are flip side words. Something is "tougher" when it resists breakage. Something is "more brittle", when it will more readily chip or break.
We might say that we want "toughness". However, for a knife edge, the third term, "hardness" comes into play.
The closer the edge brings the two faces of the blade (there's always some level of micro transition between the two faces), the sharper the knife. However, that also means the edge itself will be just that less resistant to side-to-side pressures, that can result in the edge are of the blade folding over to one side or another. Mind you, we are talking about very, VERY small cross-section areas, where forces end up concentrated. keep the edge of a knife sharp, you generally want a certain degree of hardness. Hardness involves resistance to such forces. Otherwise, the microscopic edge will just fold right over each time you try to cut something. But everything is a compromise.
Also, consider sharpening. A "tougher" steel is a steel more resistant to the abrasive sharpening process. But, sharpening is the process of removing material. So, "toughness" makes it harder to sharpen. And, often in the manufacturing processing of steel knives, "toughness" can only come at the expense of "hardness"
Now, take pruners and loppers. I'm supposing that these are tools, where the cutting edges are relatively small scissor-type cutting mechanisms with long handles (so you can use leverage through the handles to concentrate your cutting efforts).
The inner faces of the clippers are smooth, where they rub against one another. And there's a certain thickness to the blades. After all, you're cutting through branches and stems.
Ideally, you never want the clippers to break. Toughness is paramount here. The steel will probably be chosen to be tough. And each of the two blades will be thick, with edges that are easily felt to thicken right behind the edge - to resist breaking. And a good part of the design is to use wedging to aid in their cutting process.
In contrast, good quality kitchen cutlery is designed to be much thinner by far than landscaping clippers. That thinness minimizes wedging.and makes it easier for a cook to cut foods during prep work.
When you sharpen the clippers, you are sharpening just the side of each blade which is an outer side. The inner side of the blades, where there is contact, is never sharpened. (for the knife people reading this, think of it as sharpening two single bevel knife blades).
When sharpening the kitchen knife, you normally are sharpening both sides. You are also sharpening at much more acute angles. You are also using much longer sweeps on each pass on the stone in the knife sharpening process. And the degree of polish on a kitchen knife edge is much, MUCH higher than on any clipper or lopper.
The clippers will use comparatively coarse stones, compared to the kitchen knife. And for the kitchen knife, "polishing the edge" brings you to further sharpness, something that would simply be immediately destroyed in use, if you were to "polish the edge" of clippers.
I'm not saying that clippers, loppers and other landscaping tools should not be sharpened, but that the tools and techniques aren't necessarily transferable between landscaping tools and kitchen cutlery..