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 always, there are trade offs, no silver bullets.
https://mikehadlow.blogspot.com/2012/04/database-as-queue-an...
The original article handles the first argument: Postgres doesn't need polling. Instead it provides a notify mechanism, that informs the application when the table changed (something was added or removed from the queue) via the SQL NOTIFY statement.
For the second point it also provides a solution: since optimization for reading is not needed anymore with the NOTIFY statement, the trade-off like different: we now need an efficient way to write. For this the article provides an efficient update statement with special lock behavior. This helps to make writes efficient, too.
It looks like both points from the blog post you linked are handled in the original article.