I am unable to eat tomatoes. What can I use instead, especially in soups

Tomato puree is concentrated tomato. So where it is called for in conjunction with other tomato products, be they fresh or tinned, it is an attempt to increase the tomato flavour/presence in the dish without increasing the bulk or water inherent in less concentrated products.

Additionally the flavour of puree, having gone through a reduction process is somewhat different, more intense and rich than straight tomatoes.

Indeed, canned tomatoes tend to be surrounded with juice that is more reduced than would occur naturally. Which is part of why they are used against fresh tomatoes.

The tomatoes pictured are known as slicing or globe tomatoes. The conversion rate is going to depend significantly on the size of your slicing tomatoes.

While plum tomatoes tend to be rather uniform in size, a slicing tomato can range anywhere from 1.5 to 3x the size of a plum. If they're close to the size of a baseball, that would be about the 1.5x end of the range. If they're closer to the size of a softball that is the 3x end of the range.

I'm not sure what your recipe is, but you should be aware of two properties of plum tomatoes. First, they have a much lower water content than slicing tomatoes. This makes them great for stews and sauces. Second, their seeds are rather bitter; this is likely why your recipe calls for them to be seeded.

If you're using slicing tomatoes you can omit seeding them if you desire. You'll also want to cook them longer to address the higher water content.

What would honestly be a better option is to simply use canned San Marzano tomatoes. These are widely considered to be the best tomatoes for sauces. Plus they are canned at the peak of freshness, allowing you to have ripe tomatoes year round. Fresh tomatoes bought outside of summer are often lacking in flavor.