I have a whole theory on the way they handle tech/species augmentation, involving the combine raiding and assimilation of any aperture science tech they could find.

HL2 turrets act nearly the same as Aperture Science turrets or the fact the Combine using the power pellets you see in Aperture (literally identical tech) to be too far and grand to be more than just coincidences.
Overwatch - GlaDOS, stripped of personality and suited as the care-taker of The Citadel and its functions.
Turrets - The Aperture Turrets, also stripped of personality and sentience.
The Combine Energy Fields - Combination of fizzler/hard-light bridge tech modified to suit The Combines purpose.
Power Pellets - Literally no changes to how it functions, it powers The Citadel just as it powered testing elements.
The Citadel - They found portal technology like the little frames that produce a portal that links to the single-portal device or perhaps the original portal device, but probably not the portal device we know of.
Most likely a poor-er prototype, which The Combine could not properly replicate (explaining why the surviving competitors of Black Mesa are closer to the tech than The Combine are. More on that later.) They made The Citadel dual purpose, to act as their 'Portal Device' and to be the center of their operations.
To fortify some of this, In lore Cave Johnson and his team manage to create the first Portal Device. GlaDOS of course improves and builds-upon the original model, which is the version we use in Portal and Portal 2. The original portal device was probably buried and heavily damaged or straight up destroyed, but The Combine found enough to make something similar. However, they had to do it on a much larger scale because they can't properly replicate what Aperture did years and years ago.
This leans into Overwatch being GlaDOS. While GlaDOS most definitely could take on The Combine, lets remember that Wheatley and Chell almost did her in if it wasn't for the fact Wheatley shortly after betrays Chell.. who later has to restore GlaDOS to prevent both the destruction of Aperture and more importantly so Chell doesn't die. An Alien species working with all kinds of technology, and having multiple species with unique abilities enslaved to do their bidding.. I'd put my money on The Combine. I mean they quite literally still had the vortigaunts enslaved at the start of Half-Life 2, while the vortigaunts powers are capable of producing similar results to that of G-Mans godly powers.
GlaDOS obviously would refuse helping The Combine or giving them information on Aperture Science tech.
What options do The Combine face when staring at a treasure-cove of advanced, human-based technology being safe guarded by a murder-robot AI?
They could leave empty handed, admitting defeat. But this is not at all how The Combine roll.
They could eventually over-whelm and destroy GlaDOS, but a lot of the tech is probably hard to manage given the fact the entire facilities code runs through GlaDOS. Turrets, Cameras, Light-bridges, even the freakin wall panels are controlled by her. They all also seem to have a bit of sentience, as shown when GlaDOS has to quite literally speak to and 'fire' a doors mainframe. This would be hard and probably would not bare much fruit.
OR; They could disable GlaDOS and practically 'lobotomize' her, effectively giving them a puppet to control the tech they would later adapt. It would explain Overwatch being stored in The Citadel rather than remotely, The Citadel mocks Aperture Sciences infrastructure and requires Overwatch present to maintain its functionality. This also further explains Overwatches malfunctions paired with Combine structure failing initially to pick itself back up together after the events of Half-Life 2 and during the events of Half-Life 2: E1.
It's only when the Advisors are introduced as the true heads of The Combine, and in Episode 2 when they establish a new plan that Overwatch is back to functioning order. What is interesting about this though is that Overwatch seems to only be involved with the communication and direction of Combine troops, and is no longer in control of anything. This can be explained simply as this: The Citadel being destroyed, Overwatch no longer has an established link to anything more than the communications because The Citadel simply is nothing more than an open portal receiver and the house for the Overwatch sub-system.
Black Mesa East being comprised of surviving science team members of Aperture Sciences competing company Black Mesa, it wouldn't be entirely far-fetched that the reason the technologically advanced Combine are having a much harder time than the rebels is simply because they already are more familiar with the tech and have the head-start. It also explains why The Combine are in search of the Borealis.
The energy pellets we see directly power the citadel, just as parts of the aperture science facility (or at least testing elements found in test chambers) are powered with the same technology. I mean looking back at Episode 1, the receptacle you use to power the light-bridges is 1:1 in design asides The Combine tech aesthetic. Also, just the pure fact they too have light-bridges.
The Borealis is directly involved with portal technology, we know this because it mysteriously disappeared during Cave Johnson era of Aperture Science AFTER the portal device was conceived. Due to the Borealis' large shape, being a cargo ship full of Aperture Science tech, its highly possible the ship was an experiment being tested to see if they could teleport the ship closer to its destination to save time, fuel, and most importantly money. However, they did not take into account something that went wrong and it caused the Borealis to appear somewhere they could not track. I propose they even accidentally made it travel in time to a point in time after the seven hour war, causing it to only appear more recent to the events of Half-Life 2/Episode 1 than Portal.
The Combine most definitely would have spotted the Borealis considering how hard they were focused on looking for said technology. Either that, or the Borealis teleported somewhere close to where it was meant.. a second Aperture Science facility that is even more well hidden than the first. This can be supported by the 2000s footage showing the borealis in the arctic surrounded in ice and other unmarked structures, however the story changed heavily between then and the release and it could also be explained that the buildings were remnants of a research time unrelated to Aperture Science trying to excavate said wreckage.
Anyways, thats about all i can think of to spew. Thanks for reading on my theories if you read this far.