The speed loss is more likely caused by other wifi nearby Wifi networks, as Soundtouch does not create its own Wifi unless reset back to the setup mode.
Make sure that your Airport network is set to use separate ssid for the 2.4ghz and 5ghz networks and if want to continue to use wifi made sure the Soundtouch is only told about once of them to avoid automatic switching if the speed drops below 10mb/s.
If you used multiple wifis or mixed mode (automatic switching) after setting the airport as indicated about, reset the Soundtouch and reselect the Wifi you want it to remain using (use the 5ghz in the devices are in the same room and less than 10 metres away otherwise use the 2.4ghz one).
If you are able to do so connect your Soundtouch 300 by directly to your Time Capsule (or Airport Extreme) as I have done which disable the wifi and enable you find the Soundbar every time with the Soundtouch app (unless the IP address was changed, in whidh case power cycle the Soundbar).
Usual cat 5 utp cable is sufficient unless the unit is more then than say 5 metres away in which case consider sstp (shielded cable), cat 6 cable can also be used, Soundtouch networks do not require Gigabit ethernet,
if you are using Airport Express and installed the latest firmware you can enable Airplay 2 support by connecting the optical output (you may need an adapter) unless you are already using it.
Do not connect the Soundtouch to the wan point of your Airport device.