Etymology of the name Wales/Welsh in modern English: which one is the basic term?

I am interested in the way the name of Wales (and of the Welsh) has been transliterated/translated in other languages.

(I have become interested in that because, as a native Romanian speaker I have noticed the abnormal translation of that name in Romanian — more on that here. — I think that in some cases — the Romance languages, except Romanian, maybe Corsican too? — "Wales" has been translated by replacing W with G. I wonder if that is the case or not: whether the term Wales has been taken into account as such within the neo-Latin language and adapted to it, or was the G-version term first created in Latin? But that is not the question here, it would be a subject for a different question, a per-language SE question - not for this site).

All I am asking here is: what is the situation in English?

I think I am familiar with the root-word: the Proto-Germanic word walha 'foreigner, stranger, Romance-speaker', brought by Anglo-Saxons to the British Isles. In Old English, the name of the country comes from the name of the people: Wealana/Wealas means "foreigners" and Wales (like Cornwall) derives from that (more here).

What about the word Welsh in Modern English? Is it derived from the name of the country (Wales) (just like Romanian is derived from Romania) or directly from the name of the people in Old English (Wealas) (like Romania is derived from român/roman)?

EDIT AFTER COMMENT:

What happens in Old English is clear to me. The term is an adjective (foreigner) that gives the name of the people and then of the country. But in modern English it seems to me that Welsh comes from Wales like "selfish" comes from "self", "girlish" from girl, and by the way Polish from Pole, French from France, Italian from Italy, Romanian from Romania — that is: like it happens in most other (foreign) languages where the name of the Welsh is derived from the name of the country (transliterated from English).

Is that impression justified? If yes, that would be normal, many modern exonyms are created like that (Hungary > Hungarian, Wallachia > Wallachian, Romania > Romanian); while the endonyms operate conversely: magyar > Magyarország; valah > Valahia, român* > România.

Short answer:

The term Wales initially referred to the people, with Wales as the name of the country coming from that later. Welsh (the present name of the people) comes from the old adjective describing individual members of The Wales, rather than the present name of the country.

 Volcae -> Walhaz (people) -> Wælas (people)     -> Wales (people)     -> Wales (country)
                           -> Wælisc (adjective) -> Welsh (adjective)  -> Welsh (people)

As you noted, the history of the term Welsh (people) comes from the Old English Wælas, from Proto-Germanic Walhaz, derived from the Roman name for these people - the Volcae (which was almost anybody living in the Western Roman Empire, who wasn't a Roman).

Note, the group-name for the people was the Wælas, and from the same root - comes the word to describe an individual as being part of that group - Wælisc. (Similar to the group Celts, and individuals who are Celtic)

However, during this time - there was no single country called "Wales" (or a variant of).

On the island of Great Britain, we had the people (also referred to by the same Volcae/Wælas/foreigner terms) who would be known as Britons (due to the actual place they were).

When the Anglo-Saxons arrived, the Britons were slowly pushed back towards Strathclyde, Cornwall and modern-day Wales. As such, the term Wælas was now applied to the peoples in these specific regions, contrasting to the Anglo-Saxon settlers on the rest of the island.

(Note, each of these regions was still controlled by different groups, such as Strætcledwalas for the Wælas that lived around Strathclyde)

In the 13th Century, the remaining parts of these regions were then taken over by a single ruler, and the title "Prince of Wales" was given by Henry III.

Note that this is "Prince of Wales" as in "Prince of [the] Wales (people)".

From here, with those regions under control of a single ruler, fitting into the larger system - the name "Wales" appears to understandably transition from "the Wales (people)" to "the name of that region that contains all of the Wales".

(Giving the country it's modern name "Wales").

At the same time as all of this, as mentioned at the start, the individual themselves were described as Wælisc (as was their language). This then turned into the more modern "Welsh" (e.g. "A Welsh person"), which is now used as the collective noun for the people as a whole (The Welsh).

Note, as this is an English question - this answer does not mention the self-identified name Cymru, which was the name the 'Welsh' people have in their own language.

Sources:
https://wordhistories.net/2016/07/28/wales-cymru/
https://en.wikipedia.org/wiki/Wales#Etymology