What oil will support the absorption of vitamin D?

As you rightly pointed out, vitamin D3 is fat-soluble. Therefore, it is recommended to take it with a meal rich in fats, such as lunch. There is no need to consume additional oil.

It is also not contraindicated. Each natural oil has its own valuable properties and no matter which one you choose, it will certainly be a good choice when it comes to influencing the solubility of vitamin D3. It is common to find preparations with vitamin D suspended in linseed oil.

Here is an example of the preparation:

https://www.gdziepolek.pl/produkty/43037/lenvitol-olej-lniany-budwigowy-plyn/apteki

There are also preparations that contain vitamin D3 already suspended in oil, in capsule form. As a result, you do not have to use additional oils to improve its dissolution.

Here you can compare the prices of exemplary vitamin D3 preparations and order them with home delivery or pick-up at the pharmacy:

https://www.gdziepolek.pl/produkty/82436/vigantol-krople/apteki

https://www.gdziepolek.pl/produkty/105589/ibuvit-d3-4000-iu-kapsulki/apteki

https://www.gdziepolek.pl/produkty/109137/d-vitum-forte-max-4000-j-m-kapsulki/apteki

Here you will find the preparation used so far:
https://www.gdziepolek.pl/produkty/105741/vigalex-max-tabletki/apteki

You can learn more about vitamin D3 in the article:

https://www.gdziepolek.pl/artykuly/witamina-d-czyli-nie-unikaj-slonca