Hello and welcome.
It appears your CCM is at fault more than the siren. You can use a second hand CCM but it'd need recoded to your car and your key fobs need synced with it - so best install it and put it on VCDS right away. Ideally find you the part number of your current one and replace with the same as some are specific to 3 or 5 door, and in 2005 the communication protocol changed.
There are members near to you with VCDS if you don't have it, the CCM is behind the glovebox and easy to get to.
To test if your alarm is working, lock the car with the fob, wait a few seconds then unlock with the key blade. Get in and wave about to set off the ultrasonics, if your indicators flash but there's no alarm tone then your siren is gubbed.
I have replaced a few of these sirens though on my mk5's, even though they set off when intended, sometimes it'd also go off randomly. You can get a used siren for £20ish or a new one from Aliexpress for about £25. A new one from VW is about £130