if the leak is small and localized to one specific spot, it's usually worth doing a targeted repair rather than replacing everything. but it depends on how worn the rest of the piping is - if the tube is 19 years old now, the material might already be compromised in other places and the crack you're seeing is just the first sign. first give the whole pipe under the sink and in other reachable spots a visual inspection. if the rest looks okay, then just fix that section and you're done.
but if you notice rust, other small holes, or the tube feels really fragile to the touch, then it's time to think about a bigger replacement. maybe you don't need to change everything from scratch - it might be enough to replace the problem section or the most exposed stretches like the ones near the boiler or in humid areas. cost-wise, a local repair (if you call someone to seal or swap out a small piece) will run you 100 to 300 euros, depending on the plumber and how easy it is to access. replacing the entire hot water piping in a normal apartment goes for 2000 to 5000 euros pretty easily, so it's not exactly cheap.
the smartest thing is to have a good plumber check it out and tell you the actual state of things. if you notice a strange smell from the water or if the hot water keeps cutting out, that's a red flag that there might be internal corrosion. don't wait too long to get it fixed for now - a couple weeks of moisture under the sink can lead to mold and wood rot in the cabinet.