I don't think this is a tripod stability problem. The star trails are all straight, not wiggly as they would be if the camera where moving during or between each exposure. The dimmer stars are easy to see as nine distinct dots. None of the dots indicate camera movement during any of the nine exposures, and none of the lines of the nine dots for each star are distorted as would be expected if camera movement were a problem.

I think this is a focus problem that is acerbated by the time gap between exposures. It may also involve blurring due to overexposing the brightest stars. The effect of slight defocusing or overexposure is that brighter stars also appear to be larger stars. Instead of drawing a smooth arc as one very long exposure would do, combining nine shorter exposures with significant gaps in between creates lines of variable width. The lines created by the brightest stars are widest at the points where the stars were centered during each exposure, and narrowest at the points in between those centers. Similar to this drawing:

These irregularly shaped lines may be causing our eyes/brain to see the trails as blurry. There also appear to be significant compression artifacts in the image that are arranged in an almost brick like pattern of alternating horizontal and vertical patterns.

Here are some things you can try:

• Try reducing the overall exposure by reducing ISO and narrowing the aperture enough to reduce the net exposure by a couple of stops while also extending shutter speed to around 2 minutes or so. This will help you in two ways: the stars will be trails in each exposure (rather than dots) and the Milky Way will be much dimmer. Since it moves around the sky along with the stars you can't get a sharp Milky Way and star trails in the same exposure or stack of exposures.
• Shoot on a cloudless night so that the movement of clouds isn't an issue.
• Figure out what is going on with the weird compression in StarStax. I've seen images stacked using StarStax and never noticed that kind of compression before. Make sure your original images are saved as RAW files. Batch process them with a RAW convertor and export to StarStax as uncompressed TIFFs.
• Adjust your White balance so that the dimmer stars are predominately white, not mostly blue. The human eye has the most trouble focusing on the blue end of the spectrum and this may also be contributing to the blurry perception.