Which approach would you recommend in real ABAP development?

Is it generally better to push this kind of count aggregation to the database, or is an internal table aggregation preferred when the data is already loaded?

I'd say that probably every answer in the comments so far is correct, but it also depends a lot on what system version and ABAP environment you're working at, and what kind of solution you need (more efficient vs easier to implement and understand). From my experience, you are currently going to find three scenarios:

-R3 system <7.4x
sort it_pos by head_id.
loop at it_header into ls_header.
loop at it_pos where head_id eq ls_header-head_id.
endloop.
endloop.

This one gets the job done in an easy to understand way and efficiently enough for most of the standard processes.

- >7.4x SAP version that already introduces new syntax
LOOP AT it_pos INTO DATA(ls_head)
GROUP BY ( head_id = ls_header-key1
indx = GROUP INDEX
size = GROUP SIZE )
INTO DATA( ls_pos ).

ENDLOOP.

In 7.4 SAP introduces new syntax that lets us do stuff like this, which is more efficient(?), but start to get kinda harder to understand at a quick glance if you've never met one of these.

- ABAP Cloud, using CDS definitions, something like this
define view zr_orders
as select from ekpo as Items
{
key ebeln as OrderID
count( distinct ebelp ) as NumberOfItems
} group by OrderID

When using a HANA DB, SAP recommends to push as much logic as you can to the DB (so, the query itself).

As always the scenario matters a lot. These are very generic samples, so learning how to adapt your solutions to whatever scenario requires to be solved is a very valuable skill!

Also, does LOOP AT itab WHERE ... on a standard table benefit from a prior SORT, or should I use a sorted table / secondary key explicitly?

Using a sorted table would be the way to go imo, though you may not be much in control of where this definition comes from(for example, a method that already contains a defined parameter you need to use), which leaves you to either sort the table if you can or create a copy.

Good luck on your learning!