Could just be a valve too. Those are much cheaper. Had one go years ago. A stream was pissing out the side from the relief pipe. Cost about $200 to fix.

If you're in desperate need for a shower your local aquatic centre.

When our family visited my parents home country in the 90s and 2000s nobody had hot water systems. My mum still insisted on us washing in warm water if we showered at night, though. So we just boiled hot water in a kettle on the stove, poured it in with some tap water in a large plastic bucket, and used a plastic scoop to wash ourselves. We also didn't grow up with hot showers for the most part so it wasn't outrageous. However... Massive caveat this was obviously a lot easier in the tropics. But thinking back it's made me realise how much we take hot water for granted.

Anyway, the bucket method is there as a last resort...