Are Davis Cup matches accepted as official matches, do they appear in the players' stats?

Yes they are. The ATP World Tour shows the Davis Cup Finals in their official Calendar of tournaments, which links to the page Davis Cup Finals.

It is also important to note this from ATP Rankings in Wikipedia:

Starting in 2016, points were no longer awarded for Davis Cup ties,¹⁶ nor for the tennis tournament at the Summer Olympics.¹⁷

Davis Cup matches do count towards a player's official stats, head to head record.
But not all zone group matches do count.
e.g. Group IV Africa does not count.

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Most of the time, by Davis Cup people mean Davis Cup Finals (World Group up to 2019) but it is worth knowing it's a multi-layer competition.