Learn Danish: Smagningen omfatter ikke kun olivenolien, men også en bedre oliven. - The tasting includes not only the olive oil, but also a rather good olive.

This is an example of the absolute comparative. In Danish, a comparative adjective like bedre can be used without actually comparing two specific things. Instead of meaning 'better than something else', it softens the adjective to mean 'rather good', 'fairly good', or 'quite good'.

Is oliven a common gender (en-word) or neuter (et-word) noun?

It is a common gender noun, which we can see from the indefinite article en in en bedre oliven. Notice that in the compound word olivenolien, the definite suffix -en also shows that the root word olie is common gender.

How does the ikke kun ... men også structure work?

This is the Danish equivalent of 'not only ... but also'. Just like in English, it is a paired conjunction used to connect and emphasize two related items. In this sentence, it pairs olivenolien and en bedre oliven.

Could I use inkluderer instead of omfatter?

Yes, inkluderer would also work. However, omfatter is very common in Danish to describe what a program, event, or concept 'comprises' or 'covers', making it a very natural choice for describing what is on the agenda for a tasting.