Hello! Firstly congratulations 278,000km on a little 1,6tdi. They are a great engine. This is the gti forum but sure we can help.have you removed the silicate “bag” from the coolant expansion bottle ? Or does your bottle say “mit silikat” ? It’s been discussed a thousand times on here but worth removing it or at your car’s age, renewing the bottle and the coolant. Have you checked all the coolant hoses for any splits or leaks ?
Can you smell coolant under the bonnet ?
How do you know the battery is good ? Have you performed a test on it? Did you mean you charged or changed the battery ? The battery will need to be coded to the car if your car has a BCM attached to it.
Check the coolant pipes at the bulkhead, one should be hot and the return should be cold ! Are you losing coolant ? Sorry for all the questions but it’s a start ! Or else just bring it to a garage you trust and get the to diagnose it, good luck
ps. It could still be the heater matrix due to getting clogged due to silicate bag split or just be the matrix pump. Due to the design of the matrix it may feel like nothing is wrong as inlet and outlet pipes are hot, the only way to check it is to measure for temp drop using a laser temp gauge. My bet is it’s blocked