Most POE injectors "only" have Gigabit connections (some of the very cheap ones only have 10/100 Mbps). If you need 2.5 Gbit, then you have to use a special one, such as this one: TP-Link TL-POE260S (PoE injector)
Unfortunately, you can't filter by supported network speed on digitec, but the manufacturer's specifications often leave a lot to be desired in terms of speed. :P