i think corporations are still likely to exist in certain parts of the world that work in cooperation with the greater combine apparatus but are semi-autonomous political entities, such as Heckler and Koch. speaking of, my headcanon for the requirement to use the standard CP weapons (USP, MP5, MP7) is that H&K put pressure on the wider European sectors to only provide their guns
TL;DR is that this is actually practically canon as per HL:A.
We see numerous products, many old but some recent, put forth by named private/consumer entities. Most pertinently that includes perishables, hazard equipment used by Infestation Control, and even small arms manufacturers working with the CEC.
The not-TL;DR addendum, below, to that statement contains a lot of boring musings over how the empty, laughable shell of personal industry might work in the midst of a utilitarian machine like the CMB. If that's your vibe, keep reading. If not, the first three sentences of this post are about all you really need to know.
Now, based on the environmental storytelling provided in the first third or so of HL:A (up to the Golden Lion levels, give or take?), I feel like it's safe to say the "consumer goods"/private industry beneath the Combine is akin to what we see in - gasp, gun me down - 1984. Where yeah, it technically exists, but it's threadbare and exists, effectively, in three primary tiers.
You've got the ones that produce directly for/under INGSOC. The equivalent here is H&K, the hazard gear manufacturers, resource management or production areas, etc. Assets that provide a direct logistical and industrial benefit to the functions of the Combine organism. There's no sense in saying they 'dominate' the industry because the very notion of a competitive industry is an inherently farcical notion under this particular occupying force, but they're the closest (relatively) to normal function on a day-to-day basis.
After that, you've got those staples of urban life that are probably recognized, albeit barely, and provided the bare necessities by the state to function, places like restaurants/cafes. In this iteration, that'd be places like hospitals and the sort, where the Combine may offer the sparsest minimum of supply to keep them in business, but it's mostly just a formality.
And then you've got the 85% that's just ... 'If you can make it work, great'. Repair shops, brothels, etc. Largely trades and smaller business.
The Combine have so thoroughly fucked the world that mass production of anything that isn't for/by them just isn't worth the trouble of regulating or supporting, so the only sustainable kinds of personal venture - which they sure as shit don't care about
recognizing - are gonna be things like electronics, furniture, et cetera. And even then, sure, you can try to run that kind of enterprise for yourself, but good luck getting help from any official source outside of probably paying out the ass for material from contracted-but-still-a-little-autonomous shipping/logging/etc. companies.
It's the barest bones of consumer production. A mockery of commerce, a corpse not-really-trying-but-"trying" to disguise itself as economy. So based on that, based on the simple fact that it's all one big stageplay that barely manages to present itself as an industrial process, we can safely assume that the degree to which citizens or business owners are actually affecting/influencing the 'global market' - or even sector-wide market - on an intrinsic level is minimal to nonexistent.
Because even if you're John Bluesuit or Ricky Gunrunner or the closest thing to a 'proprietor' as can exist in this world, there
is no global market to begin with.
It's a sham, albeit one that happens to not step on the otherwise crushingly apathetic toes of the Combine itself, because their view of humanity's benefit to their unending expansion is strictly binary. There's only two options that don't include the designation of 'kill it'.
1. Their use and their output is either vital/useful to the state.
2. It's simply ... there, assuming it doesn't threaten to undermine or cut out the actual 'core' regime of the Combine itself.
So would any impressions of one company being more influential -
intrinsically - actually be anything more than just that? Impressions? Varying shades of what's ultimately a muddled, dysfunctional, and highly imbalanced array of sectors and consumers with which to interact?
That's the kind of question HL:A ultimately leaves unanswered, but does confirm to be a question worth asking, and a question with some ground in what we are presented with at the comparative peak of the Combine's regime. We know that there is some echo of the days of independent manufacture and some ghost of private - or "private" but ultimately connected to the state if it wants to rise above crippling logistical drought - industry.
Which may not seem like much at first glance, but it offers a fundamentally
huge amount of material for further speculation. So that's cool, I think.