I checked for my country (Slovakia in Europe) just out of curiosity:

- tomatoes (148g for 100g of ketchup)

- distilled vinegar

- sugar

- salt

- spice and herb extract

- spices

https://www.grizly.sk/heinz-paradajkovy-kecup-jemny-570-g

It does look like there's no preservatives added to heinz. It appears the lack of mold growth in ketchup comes down to a combination of lower pH from the vinegar, and low water content by cooking it out of the tomatoes. According to some food safety experts, it's possible for mold to grow on ketchup, less so for pathogens. Keeping it cold will definitely extend the time it would take mold to root.

Wrong! Both bacteria and fungi can thrive in a variety of pH. Acidophiles are a group specialized to highly acidic environments, and there are alkaliphiles as well. Fungi and bacteria also have methods to both change the pH of their environment, and adapt to it. Google it, there's plenty of research papers.

Both bacteria and fungi prefer more acidic than alkaline environments, with a "happy range" for each. Tomatoes are only weakly acidic, at 4.3 to 4.9. But molds commonly grow at pH 3.5 to 8. Aspergillus niger and Penicillium funiculosum can grow at pH 2 and below.

Extremely low pH is certainly useful at inhibiting some forms of life, but the world contains many different forms of life, and some are a lot more adaptive than others. Research shows that the best way to preserve food is a combination of chemical preservatives and low pH. Which is why the commercial food industry uses preservatives...