It should slow the internet but not stop it..
I recommend you redo the setup of the Time Capsule.
Make sure it has a short name with no spaces and pure alphanumerics. eg TCgen5
Then name the two wireless bands differently.. eg TC24ghz and TC5ghz
Then when you send video to the TV which is most likely going to use 2.4ghz since few TV will work on 5ghz.. connect your other device to 5ghz and check if the internet is still available.
I do not know what you mean by playing ps4 media server (what is this exactly.. Plex??)
Nor exactly what role the PS4 plays in this.. are you streaming to the PS4 or from media files on the PS4.
Whichever you do, getting enough capacity with wireless doing more than a single hop is painful and so you should have as much as possible connected by ethernet.