Well, I suppose we need to define country, nation, and state first.
England annexed Wales, so there must have been a country to annex. Your quote lists Wales as a country. The nation, i.e. the peoples with a common language and culture and within some borders less than the Isle as a whole could I suppose be classified as forming a country post-Roman departure, until such a time as relatively stable borders could be recognised as the geographic borders of the country that nation inhabited, so 5th century?
However, your two replies speak more to statehood/governance than nation, to me you're asking the question "when did Wales become a sovereign state" which is a very different question - and as I'm guessing you well know the UK is comprised of four countries, the UK being the sovereign state - none of the four countries are sovereign states unto themselves.
> prior to annexation it was only a loose confederation of principalities
Which I would classify as a country. The borders were stable-ish, as much as any were for their time, and the people shared a common tongue and culture. Subdividing a country doesn't negate country-hood, does it? The United States has powerful member states, and has accreted states along the way, with borders changing up until what, 1950 something?
> I've yet to find definitive details of when Wales officially became a country.
Supposing we could find an agreeable definition of "official", I'd be surprised if more than a few relatively recently formed countries can be held to the same standard. When did England become a country? When did China? "Official" recognition creates the need for another entity to be the one recognising. If we go by inclusion in ISO 3166 then I suppose Wales became a country in 2011. if we go by nationality, then one could argue it was a country pre-Roman invasion, and it has progressively shrunk its borders ever since.
> It seems Wales, perhaps first defined by the invading Romans, was then created as an entity only by the English crown's definition of the area in which "Welsh" courts could act.
Wales, as in, a collection of people sharing a language and customs, was clearly in place for the Romans to come along and see it. Unless we are getting into some metaphysical quantum country state where a country can only be a country once observed, it seems odd to say that the Romans could call it Wales, but the Welsh couldn't do so prior to the Romans turning up and having at it. As for creation by the English, again, the English annexed the country of Wales. The country was there for them to annex. Wales was not in some cat-in-the-box superposition waiting to be seen by hungry Anglo-Saxons. It existed, thus it was annexed. Regardless of its unified authority or lack thereof, a people inhabiting a space called that place home.
Fomr your other reply:
> When did it become a country? Or if you prefer more specificity: When did the region of land we today call "Wales" acquire any sort of significant unity of governance, as a totality, separate from England?
So, the question is in fact: Wales was once a country, got gobbled up and is slowly regaining some independence. When did it become a country _again_? Is that roughly what you're saying? If so, most people would likely point to 1998's creation of a National Welsh Assembly for that one.
The reason I think it is important to define the terms, is that while I - as a Welshman - wouldn't consider iron age Britain to be "Wales", I still recognise its ethnic importance on modern day Cymry. I'm no scholar, but given today's borders it's hard for me to not consider post-Roman Wales as the birth of the contemporary geographic and to some degree geopolitical country. So I suppose my answer is it became a country whenever people generally started calling it such, and it became a recognised state whenever some recognising entity recognised it as such.