Do chess AIs still use old-style opening books? (See also this related question and this related off-site discussion.)

Do state-of-the-art chess AIs still normally start games in human-compiled opening books of master games?

Years ago, as far as I know, state-of-the-art chess AIs started games in opening books. That is, years ago, to choose their first few moves, rather than calculating, chess AIs instead consulted databases of master games.

Do chess AIs still do that?

If you wish to know why I ask, more than 20 years ago, I owned a dedicated chess computer like one of these. The computer would instantly play each of its first several moves, apparently without thinking. The computer would slow down and start thinking only after


it had exhausted the book or
its human opponent had made a poor move, deviating from the book.


Nowadays, however, playing on Lichess, where the Stockfish AI is available for post mortem, I notice no obvious sign that Stockfish were consulting anything other than its own analyses.

(One suspects that various interesting things could be written on the topic. My knowledge of chess AIs is limited. I may or may not have posed the question optimally. Therefore, feel free to interpret the question broadly at your discretion.)
Chess engines are, of course, able to analyse opening positions and come up with reasonable moves, but opening books still come with some advantages:


Moving instantly in the opening saves a lot of time, which can be spent on more complex moves later on in the game.
Some more subtle theoretical moves in the opening may be missed without an opening book.


In engine vs engine testing, the overwhelming majority of games are conducted starting from an opening position, but the engines themselves are not allowed their own books.

When playing a human, many chess applications use books, but delay their move anyway to give the impression that the program is thinking. This has the advantage of allowing said application to offer a greater variety of openings, whereas relying on the engine's analysis would lead to repetitive games.

In analysis, it is common for to only start from the first move made out of book, because it is likely that moves made in-book are reasonable.

Lichess is somewhat unique in that it uses the engine to analyse every move rather than using a book for the first moves. The analyses of many opening positions are stored in the cloud to avoid duplicating work in the opening (you may see, for example, "Depth 39 [CLOUD]").