In most cases where I've seen a text field with options, usually a drop down appears automagically without a need for a dropdown icon or x
Yes, I think that would be an improvement, if it can be done appropriately. I think the reason it's not done that way now is that unlike the examples you gave, in pgAdmin we're searching for one of the existing values in the list, rather than entering a free-type value that might be auto-completed.
That's what the Yelp example shows: they have a list of options (Restaurants, Bars, Food, Delivery, Pickup, and Reservations) that show as default when there are no options typed. There's just additional features included in the GIF, sorry for the confusion. We can ignore the auto-completed examples for free type values, and have auto-complete for values that exist in the list.
Mainly, if we're enabling users to type, I don't think we need icons within each field as the drop down appearing is enough context. However, if we are not enabling a user to type, then a drop down icon should appear to show that only clicking is allowed to select an option. Thoughts?