I bought a used HP Elitebook on eBay for a similar purpose. I can browse and do video calls on a bigger screen when the fancy strikes. Pretty much any used business laptop should work. I think I paid about $300 for mine and I paid extra for particular hardware I thought was neat but you don’t have to. Only thing to keep in mind is the battery will likely be pretty worn.
I am not an expert and just cobbled this together based on a couple of searches but my guess would be that the adapter is supported by your current kernel drivers but not as well as whatever drivers Windows 10 was able to fetch. It looks to me like MX uses Debian Stable sources, so you may be able to update your kernel beyond what is normally available and see if that helps. If that doesn’t work, based on this post and this post on the TP-Link forums, there’s a github repo that you may be able to install a better driver from. To my eyes there’s fairly good instructions there, including the potential need to disable the driver you’re already using in favor of the new one once you build it.