On an established Mars colony, what would be the best ways to produce oxygen aside from using water?

The same way that made Earth's atmosphere oxygen-rich: Plants.

Animals have a natural mutualistic symbiosis with plants. Animals take in Oxygen to combine with glucose in a reaction that releases water, carbon dioxide, and most of the energy used in the body. Plants turn carbon dioxide, water, and energy (usually from sunlight via photosynthesis) into water and glucose.

Martian soil is very capable of supporting a variety of plants, so there is no need to ship earth from Earth. If you have created an enclosed environment for humans, you can put a variety of plants in there as well to maintain a breathable atmosphere. As an added bonus, many plants are edible or have medicinal properties. Food plants such as onion, garlic, kale, and sweet potatoes should all grow well in Martian soil, as long as you maintain a good temperature and water them, and since kale, cauliflower, broccoli, cabbage, Brussels sprouts, and more are all the same species, it would be reasonable to expect them to do well also.

Water is plentiful on Mars, although it may require heating or drilling to access.

The soil will need to be treated for plants grown for consumption: Martian soil contains bromine and chlorine compounds that are toxic to humans.

A Martian colony would produce very little oxygen. It would recycle it.

Moxie seems to be the go to for near future Mars missions. You can break down iron oxide or other minerals to give oxygen, you can use plants, and you can use electrolysis. I'd expect all of these to contribute to a Martian oxygen cycle, no one tech would produce it all.

However the tech that is missing is oxygen recovery and reuse. These settlements will be essentially sealed systems, recycling all the air and water and converting between the two as needed.

You dont waste water by electrolysis either. Firstly that hydrogen has many uses - hydrogen and co2 can make methane fuel (needed for rocket launches), and can also be uses to make simple plastics. But oxygen breathed in doesn't disapear, the atom will be bound to other molecules by our bodies and can be recovered from wastewater processing or co2 scrubbers and converted back to the original oxygen molecule. It can even be then recombined with the original hydrogen in a fuel cell to make some power and water.

Mars is famously the "Red Planet", because it is covered in some forms of iron oxides. It shouldn't be too hard to reduce this to extract iron an oxygen, although i suspect it will be easier to just let hydroponic plants eat away at those 95% CO2 of the martian atmosphere.

Supplying a short expedition with oxygen vs. a permanent colony is a very different task, an single expedition would need something like MOXIE but a colony will have to have plants, and lots of them, anyway.