You’ve hit it with it’s as much, if not more, about how to design than it is the software tools if you want to go beyond coasters, signs and catalog items. How things fit together is not as easy as it may appear.
Look around at all the plastic things you have that contain electronics. What appears to be a simple plastic case can take months of full time work to get just right. And it’s not because the designers and mechanical engineers don’t know how to use their software packages. A lot of it is specific to how to design a part so it is moldable (the corollary being how you join a wooden box together or stitch and rivet a leather bag), but a lot of it is also about fit and function. And then you prototype and correct. And that’s just a plastic box.
My suggestion is search the Internet for videos of how people make things you’re interested in making. This is the Internet, so be warned idiots and the eager-but-not-so-well-informed abound and own video cameras, but bad ideas can be as informative as good ones. People who know what they’re doing also love to share.
Once you have an idea of how your category of thing is made, focus on how to make it with your tool - a laser cutter. Joining things together using a sloped surface is a lot more difficult with a laser. There are plenty of threads here about how we may be able to cut slopes, but unless you’re only using acrylic you have to ask: if I get a slope, how charred will it be, how will it join, if I have to clean it how will I do that? On the other hand, a laser will make so many other parts of the process easier. For some things I think “how this type of thing is made” will change. Because how things are “properly” made is completely dependent on the tools available. Like your English teacher said, “you need to know how to use language properly before you can use it improperly.”
Remember, you don’t have to use a laser for the entire project. For what I’m interested in, I believe the laser will reduce and improve a lot of things, but I will still be using non-photon based tools to complete the entire project.
And I would do the learning and the designing side-by-side. The brain learns by doing, so get an idea for something really simple and then struggle with your software design tool. As you implement your research in your design tool you’ll run into practical problems. That will lead to research on how to fix your specific issue. And so on and so on.