1. SELECT item_id WHERE expire = 0. If this is empty, no items are available.
2. UPDATE SET expire = some_future_time WHERE item_id = $selected_item_id AND expire = 0. Then check whether UPDATE affected any rows. If it did, item_id is yours. If not, loop. If the database has a sane optimizer it'll note at most one document needs locking as the primary id is given.
All this needs is a very weak property: document level atomic UPDATE which can return whether it changed anything. (How weak? MongoDB could do that in 2009.)
Source code at https://git.drupalcode.org/project/drupal/-/blob/9.2.x/core/... (We cooked this up for Drupal in 2009 but I am reasonably sure we didn't invent anything new.)
Of course, this is not the fastest job queue there is but it is quite often good enough.
As a capability, compare-and-swap has an infinite consensus number [1], meaning it's sufficient to implement wait-free consensus algorithms with an arbitrary number of participants. That makes it a perfect fit for managing a scalable pool of workers that need to coordinate on consuming from a queue!
[0] https://en.wikipedia.org/wiki/Compare-and-swap
[1] https://en.wikipedia.org/wiki/Consensus_(computer_science)#C...
Saying this as someone who has been on both sides of that interview question, and also evaluated performance in it as a hiring manager.