The question asks about a laser cutter, but also asks what kind of machine is normally used and recommendations. What's normally used is not a laser cutter. These kinds of items are likely injection molded. It also might be possible to stamp them out of sheet material in a press.
To make them yourself on a small scale, with a computer-controlled hobbyist machine of any kind, will be a bit slow, since these all need to trace the pattern, either slowly or many times.
You could use a laser cutter, as Chris Rogers suggested, and the pros and cons have already been covered.
I would be surprised if a hobbyist blade-type cutting machine could handle 1.5 mm PET (whether it would work at all, or if it did, would quickly wear out or break the machine). I'll provide some context as to why.
I've never tried it on a cutting machine, but I have tried manually cutting patterns out of PET sheets from the walls of soda bottles using a hobby knife. It is hard to initially penetrate the material, and then the cutting resistance is much higher than paper, chip board, or vinyl film, the materials the cutting machines are designed for.
My soda bottles had a wall thickness of about 0.2 mm, so the material in the question is 7-1/2 times as thick as that. PET 1.5 mm thick is a hard plastic panel, not a film or thin sheet.
Also, when you cut something like a paper product or wood, you cut the fibers. The fibers aren't stretchy, so you also get some tearing as the blade pushes the two sides apart. If it's thick, several passes will separate them all. On a thin vinyl sheet, you cut through it.
On thick plastic, some of the blade action is just distorting the plastic. It stretches rather than tears when the blade pushes it apart, and it partially returns when the blade is removed (it doesn't all stay "cut"). So even if the machine is capable of penetrating the plastic, it would be likely to at least require a lot of repeat passes after the machine thought it was done, and the edge of the cut would be full of burrs and threads that would need to be cleaned up.
If you want to make these out of 1.5 mm PETG using a reasonable cost, computer-controlled, hobbyist machine, I would suggest 3D printing them.