How do I clean an old bathtub?

Here is a tutorial for a cast iron sink that would work using the same technique https://www.hometalk.com/diy/clean/house/how-to-clean-and-remove-stains-from-an-old-cast-iron-sink-24989178 If that doesn't get it good enough you could paint it but you'd have to use very specific steps. You can find instructions here https://www.wikihow.com/Paint-the-Bathtub

How to Clean and Remove Stains From an Old Cast Iron Sink

The porcelain has lost its gloss finish. It will have to be replaced. That is the only "PERMANENT" solution. And don't let anyone tell you, that you can paint it. THAT IS A LIE!

Using a steamer may help loosen the deep dirt and stains. Oxiclean makes a foaming cleaner that also helps eat organic staining, rust, etc. with a mild scrubby pad used in circular motions. A 90 yr old tub might need professional resuscitation.

It is as clean and sanitized as it is ever going to get. Over the years, and unknowingly used the incorrect products, the original shine and finish has been scrubbed off. Mistakenly people mistake scrubbing as "clean" when in fact it is totally unnecessary. Your options now are to have the tub reglazed or replace. Bleach is one of the worst products to use for any bathtub surface as it eats away at the finish. There are other products to use that will still get rid of germs yet not destroy the finish. Worried about germs? Swish around some vinegar or alcohol.

That old it's probably cast iron. You'll need to paint. Check with someone at a paint store as to type of paint to use.

Here's a post that might help https://www.thisoldhouse.com/cleaning/22331616/deep-clean-a-bathtub#:~:text=Mix%20%C2%BD%20cup%20bleach%20into,not%20to%20splash%20the%20bleach.