The ticket (QR-code) does not guarantee you a seat. It is recommended not to activate the pass in advance because as soon as a day starts it cannot be cancelled.
If the train requires mandatory reservations and you travel without one, either you won't be able to get to the platform or you'll get a big fine.
Which route (+ travel date) are you looking at ? There are often alternatives : reservation-free regional trains or high-speed trains but for a shorter leg.
As a rule of thumb : Interrail website is not reliable so it may not mean that the train is sold out.
Without giving specifics we cannot give precise answers..
In most cases if the app says you require reservations then that is the correct situations, without reservations you are not allowed travel.
This page gives details of sources of reservations for many countries
Also this
https://community.eurail.com/train%2Dconnections%2Dreservations%2D47/how%2Dto%2Dbook%2Dyour%2Dseat%2Dreservations%2D13709