You're making assumptions beyond the problem statement.  The problem never says pressure is constant, so a temperature change does not imply a change in volume.  (An inferred change in particle number could also change the density, but I'm guessing that wasn't your mistake.)

Wouldn't simply banning TikTok constitute a bill of attainder?

Did you send this to the authors?  Most academics would jump at a simple tweak for a new publication.

Doing this can send out a jet of air above your thumbs.  If you send this jet into your mouth, you can change the pitch by changing the shape of your mouth, which I found endlessly amusing as a kid.

An unconditional right to bodily autonomy also implies the right to prostitute yourself and sell your organs, not to mention try whatever drugs you want or purchase corrective eyewear.

Measuring energy consumption is cheap and easy with a $30 Kill-a-Watt: https://www.amazon.com/P3-P4400-Electricity-Usage-Monitor/dp/B00009MDBU/ref=sr_1_3?crid=2F9E51CGW3ZDS&keywords=kill+a+watt&qid=1656014636&sprefix=kill+a+watt%2Caps%2C107&sr=8-3

I propose a follow-up experiment to measure daily energy consumption alternating hose configuration with the same set temperature.  The previous experiment tried to answer "how much does maximum cooling power change between configurations," while here we would answer "how much does efficiency changes between configurations."

Potential issues:

1. If this causes your unit to run at different power levels, you would also capture any efficiency change based on the power level, but I would guess your unit regulates simply as on/off (check the (instantaneous) power consumption with the Kill-a-Watt to be sure).
2. If one configuration works faster, it may not do as much work on the other side of the room before the unit senses "cool," and turns off.  Fans in the room increasing circulation will mitigate this.
3. I don't know how many days you would need for good statistics to smooth over all the day-to-day environmental changes.
4. You should also analyze weekend vs. weekday, and possibly exclude one.
5. You will need to monitor that both configurations actually are up to the task.

I'm not sure I want to register an advance prediction, but if OP agrees to do this, I will at least put some thought in towards one.

I'm not so sure a central air system wouldn't be up to the task.  I calculate this purifier at 150 CFM from the product page and assuming 8 ft. ceilings, and this implies 1,500 CFM would be a fairly typical residential HVAC system, so that seems roughly adequate to me.

Also, that product page suggests you should cycle air 5 times per hour, but that seems excessive to me.  I use that unit in a much larger room on a low setting and it does just fine getting rid of any smoke smell from wildfires.

Though I love the idea of a filtered ceiling fan that's out of my way and can therefore be larger and quieter, I don't think a jury-rigged solution would work at all.  Fans tradeoff flow for static pressure (https://blog.orientalmotor.com/fan-basics-air-flow-static-pressure-impedance), and I'd bet ceiling fans are optimized for flow.  The filters will up the impedance considerably compared to basically open air, and the flow would drop dramatically.

Also, some (most? all?) central air systems can run fan-only (no heat or AC), making additional filters unnecessary.

I would not have predicted that.  I don't think I've ever seen a power brick not rated for multiple voltages.  If I ever find one, the first thing I would do the next time I'm in a 240V country is plug it in and see what happens, but please don't do that yourself unless you know what you're doing.