I haven't worked in Photoshop, so it's hard for me to give an authoritative opinion. However, when I edit something online, I haven't found any tasks that couldn't be solved by the internet itself or by plugins for it, and there are quite a few of them. But I can't compare.

I won't pretend to be an expert either; I'm not that familiar with Paint.NET to make a proper comparison.
But from what I've seen, it seems like the program is significantly inferior to Photoshop. It has fewer features, and tasks are not performed as "cleanly."

Just off the top of my head, does it have a "stamp" tool, the ability to blend layers in various ways (i.e., color, screen, lighten, etc.), image editing by levels, and is it possible to work with 3D? I strongly suspect not.
And, to put it briefly, Photoshop is a professional program, and Paint.NET is not. At the same time, Photoshop is not more difficult to learn; if you don't immediately delve into the intricacies, it's actually more convenient. In my opinion, it's better to get used to professional software or its competitively capable alternatives right away.
And it's not about the fact that it's free; I've seen many people create amazing things in Blender, but I haven't seen anyone doing truly complex image work in Paint.NET. Therefore, I wouldn't recommend it to anyone.

In the same way, theoretically, you can write code in Notepad, right? But should you?

Added 18 minutes later
And for people who are specifically involved in texturing or editing textures, Photoshop is already a thing of the past. These people need to switch to Substance Painter, draw directly on the model, and use procedural texture generation.
Here's a short tutorial by someone who's not very skilled, about Painter; it's suitable for getting acquainted with the program.
https://m.youtube.com/watch?v=llZlQni46IA

The question is not about being "in the know" just for the sake of being in the know, but about not digging a hole with a shovel when there's an excavator nearby. You'll get tired quickly and won't see all the possibilities that you could have.