Ledger line thickness

I’m not questioning the quality of the printer itself. But if you’re having problems printing staves, something is going wrong. Could be a bad ink cartridge, could be a bad device driver, could be bad settings you’ve made in the printer properties, who knows. But verifying on another printer is an important step in solving the problem - you absolutely should not have to resort to using abnormally thick staff lines.

How do you create your PDF?

To answer your question: staff line thickness does scale with the scale in page settings. To keep elements of the score display proportional, the scale setting scales everything that has a size setting in sp, including staff line width (and noteheads, and stems, and clefs, and time signatures, etc. etc. etc.).

The final staff line width is simply the staff line width in sp multiplied by this scale setting - see my calculation above. The same logic applies to most other elements to keep elements in proportion. If you want to keep your absolute staff line width the same when you reduce the scale, you need to increase the staff line width in sp (like you did, from 0,08 to 0,10). However this would alter the proportions between staff lines and other elements - which might or might not be desirable.

(hints to developers below)

This same scaling issue came up in the 70s to 90s when computers started describing typefaces in terms of arbitrarily scaleable curves instead of fixed size pixels: it was realized, that when typefaces are scaled down, some parts can become too small to see properly, hindering legibility. So instead of just mathematically pure scaling down of the letter shapes, parts of letters needed to be thickened or made bigger to still look good and stay readable. (Similarly, when scaling up mathematically, things also looked odd, and needed adjustment to look good again.) American computer scientist and polymath Donald Knuth did this in the 70s-80s with his metafont https://en.wikipedia.org/wiki/Metafont package to arrive at beautiful (visually consistent, easy to read) type regardless of size for his mathematical publications that required many small symbols for superscripts and indexes but needed to stay very legible. The commercial market came to the party of curve-based typefaces later, in the 90s, and eventually realized the same thing: things need to be adjusted in shape beyond just scaling up or down. The prevailing solution was from then market leader Adobe called "Mutliple Master", of which the Wikipedia page has a demonstration: https://en.wikipedia.org/wiki/Multiple_master_fonts - this has now been adopted into current typeface standards.

One would expect the same logic - that things need to change in weight when scaled to "look good", that is, be easy to read - would apply to scaling any kind of graphics to be viewed by humans, not just type alone. Including musical score notation.

MuseScore does not do such "optical" adjustment yet, and it currently scales things up and down purely mathematically. To put a long story short, this is why, when you scale your score down, some things - including your staff line widths - will end up being perceived as too small/thin.

The problem then is almost certainly not with the PDF itself, but with the program you are using to print it. Eg, Acrobat, Foxit, Sumatra. These programs will mostly have settings to control the resolution they print at but also how they handle fine lines in particular. The latter option may have the word "antialias" in it. Probably changing those settings will help. Or just try a different PDF program. Or just skip the PDF and print directly. Any of these are better than a 25% increase in the thickness of the staff lines (from 0.08 to 0.10), which will adversely affect readabiltiy.