How to store blanched tomatoes?

I think you are not doing yourself any favors by pre-blanching.

A whole tomato is a rather durable product. It is alive, and protects itself from bacteria - they can't penetrate the skin, and if a few of them come inside, the living cells have some limited protection. It can keep for a long time at room temperature.

A blanched tomato loses all its protection and turns into a highly perishable product. The skin is gone, the damaged cells are welcome food to all bacteria. It can't be kept without refrigeration. Which is your first problem, as the taste of tomatoes deteriorates a lot with refrigeration, some of the strongest tomato aromas undergo irreversible chemical changes when stored under a certain temperature (I think the limit was around 10 celsius). Even if you store them in the fridge, they are likely to get unpleasant after 3 days, I don't think that stretching it to 5 days is a good idea.

You can of course freeze them, which will make them more durable. But 1) you will still have the taste deterioration problem, and 2) you mentioned in a comment that you don't want them to become soft. But there is no way to prevent plant matter from becoming soft after a freeze-thaw cycle, as far as I know not even industrial flash freezing will keep it in the original state, and you can't do this at home anyway.

You can choose between tasty or convenient tomatoes, but you can't have both.

You should be able to refrigerate them or 3-5 days per Still Tasty, or freeze them for 10-12 months.

I would simply put them in an air tight zip type bag for either the refrigerator or freezer (portion them into usable amounts if freezing, since they would be very difficult to separate). No additional water or oil is required.

If you freeze them, some deterioration of the texture may occur, but they will still be well suited for purees, sauces, and so forth.

To thaw frozen tomatoes, use any of the generally safe techniques. if you ahve the time, putting them in the refrigerator is fine. You can run them under cool running water (the zip bag would protect them from water logging). Microwaving should work as well, although you want to do it slowly to avoid cooking the outside while the inside to of the mass stays raw.