You can do some research and find stronger routers for Wi-Fi from Asus, Ubiquiti, etc.
You can also expand coverage with WAPs e.g. Wireless Access Points. Lots of brands to choose, but Ubiquiti is common. Run cat6 cable in attic or crawlspace from router to somewhere central and install WAP in ceiling. 2000 sq. ft sounds like at least 2 WAPs one at each end or one on each floor.
You can look into mesh networking devices but they increase latency and can be unreliable.
I have a modest 2-bay Synology NAS connected to a Lenovo office PC from eBay that runs jellyfin. It works great. I don’t use the other services you mentioned.
A standalone NAS can do what you want. But it depends on your needs and how much you want to spend. How many concurrent clients? How many transcodes at once then? Transcoding 4K (this is very expensive)? All on NAS or NAS + PC?
My understanding is you can transcode using ram or ssd. And the size should be at larger than the size of the file. So 25GB file transcoded, you should have 25GB of ssd or ram available. This is per stream. So now you see how ram is expensive to transcode with, especially with multiple streams.
If transcoding a couple 1080 streams then a cheap office PC off eBay with Intel quicksync that is at least Skylake should work e.g. i5-6500T (this is what I have). You should be able to run those other services just fine. If direct streaming 4K there is not even overheard because no transcoding is happening so that should be fine too.