How can I sort entity type query results with pseudo values?
Some thoughts... 

You should be able to do aggregation in your queries; try looking at QueryAggregateInterface and ConditionAggregateInterface. However this interface does seem to be pretty simple. The Views plugin implements full 'having' and 'group by' functionality, but probably in a way that's difficult to access outside views.

You might investigate using the Symfony Doctrine class or plain PDO to do it the 'old way'.

I am pretty sure you won't be able to calculate based on an external API; the database needs all the values to hand, either in a table or as query-provided data. Some databases do support advanced functionality like REST queries, but any code doing this won't be portable and so won't be available as standard in the Drupal interfaces.

You could possibly do the API lookups in advance (in e.g. php) and then pass them to a temporary table for the DB to check.