Making tomato mix thicker without surge in calories

Your "drink" sounds a lot like gazpacho. When making gazpacho, bread is often blended in, primarily to increase the viscosity...not necessarily "calorie thin", but an option. Olive oil is also emulsified into the mix, creating an enjoyable texture, and adding to the flavor.

The reason that your "drink" is thin, is that you are not removing the water and seeds from the Tomato. Peel them and take away the water and seeds before you put them in the blender. Go here https://www.deliaonline.com/cookery-school/techniques/how-to-skin-and-de-seed-tomatoes

One alternative, instead of adding thickeners, would be to remove some water. As mentioned in Keith Ford's answer, you could remove some water manually by de-seeding the tomatoes.

OTOH, there are various ways to systematically reduce the moisture of the smoothie itself:

• The old-school approach would be to reduce it in a pot on the stove. That is, keep it just barely simmering, uncovered, for a long time, to evaporate off a bunch of the excess water. This does, of course, imply that the result will be cooked, which may not meet your criteria. (Side note: if you are okay with cooking it, you can get a lot of thickening out of a small amount of starch by mixing it in cold and then cooking the whole thing for a few minutes.)
• A classic, no-cook, but still time-consuming option would be to pour the stuff into a food dehydrator, using the liner sheets that are used for making fruit leather from fruit purée. The heat in a dehydrator is low enough that you're not cooking anything, just speeding up evaporation. If your objective is a thicker drink, as opposed to a 'leather', just take it out after a fraction of the time given in fruit leather recipe instructions.
• The quick, easy way to make a thicker smoothie without using a thickener is to use a juicer instead of a blender. Juicers separate the liquid and the pulp as they go, so you can easily just take the heap of pulp, mix however much of the liquid back into it as it takes to get the consistency you want, stir well, and dispose of the leftover liquid any way you like (down the drain, use as cooking liquid, etc.).

I suggest adding flax meal. This is very high in fiber, but not very high in digestible carbohydrates. It won't take too much, so the surge in calories won't be so bad. You will have to measure it out. Unfortunately, the Omega oils in this have some calories.

The option that better fits your criteria is psyllium husk powder; plenty of thickening and fiber, yet almost no calories. 30 grams will be 100% of your daily fiber, but just 100 calories. That would make your drink plenty thick, with not to much taste.

I prefer the way flax tastes though, and it is super healthy with Omegas and protein and such.

There are some more things to add on this list; perhaps Chia? I haven't tried them all, so can't comment on them. It might be worthwhile to research each individually.

A super-easy solution with an ingredient many people have in their house:

Mashed potatoes.

I've successfully used a bit of mashed potato to thicken salad dressing, it might suit your needs here. (You can even buy dried mashed potato powder, which thickens stews nicely but has usually had most of the nutrition processed out of it.)

I also sometimes sweeten soups with sweet potatoes, but they have a more noticeable flavor that doesn't fit your list.