Is taking a long hot shower considered extravagance if its purpose is just to wake up or relax? How long can this shower be before it would be considered excessive?
Bismihi ta'āla
No, it would not be considered extravagance, or waste, as long as you do not prolong your shower, wasting water and electricity/gas.
There is no shar'i limit for how long you should take a shower. It would just be common sense. A shower should not take more than 3-4 mins. The sunnah of the Prophet (s.a.w.), is the water used for a ghusl should not be more than the amount of a jug of water.
And Allah knows best