Sewage systems are not garbage disposal. They're an important public health system to remove faecally contaminated waste away for treatment.
There are tests for "flushable", and paper stemmed cotton buds don't pass those tests.
https://www.water.org.uk/policy/environment/waste-and-wastew...
Here's a PDF of a protocol. https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web...
It would almost make you want to take an Advil.
Why would it be "quite depressing" if Americans call them Q-tips or "cotton buds" or any number of a dozen other things.
Given that "cotton bud" appears to be a relatively recent British quirk (gaining popularity in the last couple decades), I would submit that "cotton swab" is the original and proper generic term.
British English: https://books.google.com/ngrams/graph?content=cotton+swab%2C...
American English: https://books.google.com/ngrams/graph?content=cotton+swab%2C...
English overall: https://books.google.com/ngrams/graph?content=cotton+swab%2C...
(Refresh the page if the graph doesn't load at first.)