Ketchup is my jam.

If we are to accept the madness of treating tomato as a fruit culinarily (although, your comment makes a strong argument for not doing so), would it be a jam, jelly, or…?

How many jams, jellies, marmalades, or confitures do you know of that contain vinegar, savory spices, and salt? In a recipe calling for jam, would you replace it with ketchup?

There are several chutneys that include vinegar. They aren't in the same category as you listed, but the parent included an ellipsis, which I'll include chutney under.

Some "fruit preserves" also use vinegars and other acids. Which leads to the Venn diagrams of the definitions of pickles, chutneys, and preserves (fruit) all have a massive overlap and ketchup is right there in the middle as pickled tomatoes, tomato chutney, or tomato preserve depending on how much you want to classify it is a fruit, vegetable, or "it doesn't matter". (I would at least argue that "preserve" is the more accurate fruit term over jam or jelly.)

>In a recipe calling for jam, would you replace it with ketchup?

if the recipe was for French fries and jam: yes.