using multiple cables like that is called link aggregation. This requires BOTH devices to be capable of it. It only helps if you have multiple streams trying to cross that path as each stream gets assigned one cable.
depending on the model of switch you have. some have a designated uplink port while most of the newer ones all the ports are the same and it doesn't matter which one you use.
if you use cat6 then a 200ft run is NOT a problem at all and will NOT hurt speed.
(other than the mention of a staple... please use plastic loops instead.)
https://www.amazon.com/dp/B08B4G2784?th=1
if the wall is finished already then those sticky hooks work well to hold up cables.
Are there more direct paths a cable could take? such as through a floor in a closet or down the inside of a wall?
If it doesn't have an AP mode in the settings you can manually put it in AP mode.
https://www.cnet.com/home/internet/how-to-turn-an-old-wi-fi-router-into-an-access-point/
But since it sounds like you (OP) hasn't bought anything yet then probably easier to buy an Access Point device instead of another router.
what speeds is your ISP providing you?
Do your PCs and NAS have the capability of utilizing the higher speed ports?
Are there router settings that you want to be able to adjust that you currently can't?
Is the only reason so that you can achieve faster connection speeds between your NAS and PCs?
yes. If you get another AP that will use the older security standards and connect that to your router it will let you get those devices back onto your network.
I don't stay on top of the current state of wifi security so I don't know if doing this would be a not so great idea security wise, or if it would be a horrible choice security wise...
a small network switch is the right answer here. skips figuring out windows settings and doesn't rely on your PC being on.
something like this one should do just fine for ya. :)
https://www.amazon.com/Ethernet-Splitter-Optimization-Unmanaged-TL-SG105/dp/B00A128S24/?th=1
when mine was initially setup I had intermittent connection issues. I was able to monitor the Rx power and see it fluctuate. (the numbers to the right of the decimal are not displayed correctly which took awhile to figure out)
0.16 is ACTUALLY 0.016
0.160 IS what we would typically write as 0.16
its showing how many thousands and not padding the zeros correctly.
I called and a tech came out and cleaned the outside house box connection, the connection at the street, and the connection on the other side of the street. been solid since then.
Tucking ethernet under/along baseboard trim can be a legit option depending on ages and preferences of others in the house.
If you own the place, you could also consider drilling a hole through the floor at the edge of the room as well if the space below is unfinished.
depending on what the upstairs connectivity requirements are moving all the wired connections to the basement and just using wifi for the rest is a very legit option. I've done that in the past when my office and gaming pc were in the basement and it was only the Roku and phones and tablet on wifi used elsewhere.
getting newer hardware isn't a bad idea. But your issue MIGHT be able to be solved by turning on some QoS settings and prioritizing the video meeting and gaming devices.