How can a scratched metal bath that is tiled be repaired?

You can have the paint professionally removed and repainted, but by the time you spend money for that, you can buy a new one. Tubs aren't that expensive and last for years. Go to Home Depot or Lowes, buy a new one and have it installed.

See if this helps you decide. Granted these are US prices, but I am sure you can Google and find similar in Australia.

https://www.homeadvisor.com/cost/plumbing/install-a-bathtub/

Plus the cost of the bathtub itself, plus new fixtures, plus a plumber.

https://www.homeadvisor.com/cost/bathrooms/refinish-a-bathtub/

My vote is for PROFESSIONAL reglazing. I have had a number of tubs reglazed and with proper care, can last another lifetime.

For example, I had my mom's tub reglazed (back in 2007) as it was original to the house (back when they used quality products and had pride in workmanship - house was built in 1925), I paid less than $500 to have the tub reglazed. To replace would have been several thousand dollars.

Do what you think best for your situation and what works with materials and services available to you and what works within your budget.

A metal bathtub? I know of ceramic, enameled, and fiberglass. Is this a special kind? Just curious ☺️

Hopefully this will help! https://www.youtube.com/watch?v=CxOPQ5Xoeec