Is next to an adverb

Yes, idiomatically it can be an adverb, meaning nearly or practically

(e.g. next to impossible).

The pair can also be a compound preposition that means "adjacent."

It can be an adverb, when used to mean "practically" or almost.

(Getting a seat on the bus is next to impossible.)

It is usually a preposition, meaning adjacent.

(The table is next to the wall.)