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Yes. Most definitely, yes. If you push the scanners too hard, they will overheat and eventually die. The scanned image will look terrible, and sometimes you can hear the scanners start to whine, or worse, to make a screeching sound. If you hear this, stop the output! Driving the scanners into resonance can destroy them.
Normally you will have plenty of notice that you're getting close to the limits of the scanners, because the image starts to look like hash. Also, most scanners that are rated for at least 30Kpps speeds have either a high-current cutoff (polyswitch) on the scanner amp or they have a thermal overload circuit. Either one will shut down the amp. In most cases this will prevent permanent damage, unless you keep tripping the circuit over and over...
Hmmm. A quick search suggests that you probably paid less than $400 for this projector, and it is rated for 1.5 watts of output. That's most definitely a "cheap" projector. Based on the pictures I saw, it looks like the scanners in this projector might be capable of 15Kpps speed AT BEST, and might only manage 10K or 12K. If you were running Modulaser at the default of 30Kpps, you absolutely were pushing the scanners
way too fast.
Fortunately, as long as you didn't leave it running like that for too long, it's possible that the scanners are still OK. Try reducing the scan speed to 10Kpps and the image size to 20% and see how they look. (Note: the image will flicker more at the lower scan speed - this is normal.) See if the test patterns look better at the slower speed and angle. If so, then you've found the problem - just keep the speed lower and you'll be OK.
Keep in mind that your maximum safe scan speed is also limited by how wide your scan field is. If you have the image size at 100%, your maximum speed limit will be lower. If you reduce the size to 20%, you may discover that you can bump the speed up a few K. (Which is why I suggested you start at 20%.)
Abstract patterns (so-called "lissajous" or spirograph-like images) can be very complex. It is easy to exceed the capabilities of even a good set of 30Kpps scanners when displaying a complicated abstract. The whining noise you heard is probably not a good sign.

True, most abstract patterns will generate at least a little whine - even on 30Kpps scanners - but it should be a soft, subtle tone. If you noticed the whining as soon as you started displaying the image, and especially if it was loud, then yeah, you were over-driving the scanners. (Try not to do that...)
Describe what the image looks like when you tell the projector to draw a circle... (Got pictures?) And does the circle look any better if you reduce the scan angle?
Sadly, yes. If you have toasted the scanners, they will need to be replaced. I suspect you won't get very far with customer support on AliExpress. Fortunately, if it comes to that, you can probably install new scanners yourself (assuming you're not afraid to do a little re-wiring inside, that is). This might also be a good time to upgrade to a set of scanners that can handle true 30Kpps speeds. For around $250 or so you can install a set of scanners that will work *much* better.
That might be my scanner tuning tutorial...

Re-tuning may help if the scanners overheated and something changed internally. When scanners overheat, the magnets can lose strength and the bearing/shaft clearances can change, to name just a few concerns. Provided these changes aren't so bad as to make the scanner useless, a re-tune can sometimes compensate for them. However, I would rate that as a last resort option.
Normally people re-tune scanners to correct a bad tune from the factory or to correct for scanner drift due to normal wear and tear. Less often they re-tune because they changed one of the mirrors and the rotor mass is now different. But trying to re-tune to correct a mechanical failure is not going to be very effective.
This is starting to sound more and more like you wiped the scanners.

But we need more information to be certain. It would be best if you could test the projector at a known scan angle and known scan speed.
I'd like to see a picture of what the laser media test pattern looks like at 8 degrees and 10Kpps, if you can do that. (8 degrees means that the image size should be 14 cm tall and 14 cm wide if the projector aperture is 1 meter from the wall.) If that looks OK, then try it at 12K, and then 15K. (same angle)
If you can't do the laser media test pattern at 10K and 8 degrees, something is definitely broken...
Adam