I do not agree with your statement "image’s pixel size and resolutions are not tied to each other", in fact the opposite is true. The dpi setting is directly translated to the pixels, it has to be, whether in the file or later by interpolation by the printing or display method.
Well, yes and no. It was loosely worded on my part and I apologize - that's what I get for posting just before bed. Over the years, I have spent a bit of time explaining to people display resolution vs print resolution vs media resolution (and you probably have as well.) If it was easy, the situation wouldn't exist where people are upset that their printouts are blurry on paper when they looked fine on their device screens where the images were downloaded.
I'm just trying to help clarify how one might explain this resolution thingy to people who are new to laser engraving, new to image editing, and have no idea that the output media type might also affect the equation. Although a fact or equation might be simple, sometimes understanding is quite tricky.
Let's take the attached PNG for example. It's a 500x500 pixel, 50x50mm, 254 Pixels per inch, PNG.
In Photoshop, if I select Image > Image Size, the dialog box looks like this.

Following your statement where the "dpi setting is directly translated to the pixels" - I'll change the Pixels/inch setting from 254 to 300 and voila! Your statement proves true. The image is automatically adjusted by Photoshop to 591x591 pixels.
But...
Now I edit the pixel dimensions for width and height back to 500 x 500. Now my resolution is 300 Pixels per inch, and the image's pixel dimensions are again 500x500, but my document *physical* size is 42.33x42.33mm.

We both understand that it's because the pixels are now physically smaller, but that's not generally obvious to someone new to this. (eg. "Pixels can be smaller? I thought it was just a dot on the screen...") It *could* be seen that I've retained the same 500x500 pixel dimensions for both images and yet the resolution setting is different. That's what I was trying to say originally (badly.)
Yes - the "dpi setting is directly translated to the pixels, it has to be, whether in the file or later by interpolation by the printing or display method" statement is absolutely true. And yet, kinda confusing... because one can keep the same pixel size AND change the dpi/ppi setting. Yes, it's obvious that the "document size" changes as a result of this, but unless folk have a design or print background, what does that mean? I imagine that a very common use-case might be people downloading raster images off the web, and then try to engrave - and those images might typically be 72 or 96 dpi. I can even imagine that they'll bypass any image editing program, load them straight into T2Laser, set the resolution to 0.1 and output size to be 6x4 inches etc, only to be disappointed that their engraving is so blurry.
And then we get to the output media's native resolution. It's not immediately intuitive for a person new to laser engraving that the type of material being engraved has a natural limitation on resolution. eg. slate has a low output resolution, acrylic and mirror has a high (254 or higher?) resolution, different types of paper have different resolutions (254dpi for origami, but maybe 120-ish for watercolour paper), MDF might have a 200dpi resolution and different wood grains densities and even the direction of the grain will affect the mid-to-low resolution.
I don't know if you want lengthy stuff like this in the T2Laser manual. I figure it would make a better customer experience if there was a explanation or tutorial so that it was less confusing up front, particularly to newcomers of laser engraving with no print or design experience.
All the best,
- Ian