This is a bit of an oversimplification. Arthur wasn’t Welsh in the sense that Wales and the Welsh language didn’t exist in the time he supposedly lived. He was a Briton. Anglo-Saxons called Britons and other non-Germanic people “waels” which means foreigner. Once the Kingdoms of England were established, the kingdom of the Celtic Britons in west west Britain was called Waelas which became Wales.
In addition to Caerleon, Arthur is also associated with the region of Lloegyr in southern Britain, which is now England. Thus “England” in Arthurian literature is a gloss for Lloegyr in the tradition of using contemporary place names for geographic regions.
Indeed, if Arthur was real, he probably had many Anglo-Saxon subjects. The Britons v Saxons conflict wasn’t as black and white as later depictions make it out to be. The Saxons didn’t arrive in Britain as a conquering imperialist force. They were scattered groups of refugees fleeing west from Attila the Hun. The more common reality was probably British kings fighting each other with Saxon mercenaries and civilians on all sides. The first few kings of what would eventually become the kingdom of Wessex had Celtic British names like Cerdic and Cynric. There is even a fairly convincing theory that Cerdic was the real Arthur, which would make him equally an English and Welsh (Briton) historical figure. (1)
The round table has been suggested to be based on the Caerleon amphitheater:
There is a dispute over whether or not Percival was derived from Peruder or vice versa or if they were separate characters who became conflated. Welsh, English, and Continental Arthurian traditions overlapped in time and influenced each other.
Lancelot, as we know him, is a French addition, but cases have been made for a Celtic origin. He could be derivative of the Irish god Lugh Lamhfada or his Welsh equivalent Llwch Llawwynnauc. Another possibility is Anguselaus or Anselaus derived from a latinization of the Pictish Unguist. (2) There’s also the Breton Lancelin.
The affair between Lancelot and Guinevere did come later, but there is precedent in her affair with Medrod (Mordred) in the Welsh texts (see Geoffrey of Monmouth).
Calling the Lady of the Lake a Welsh character is particularly egregious, given that she first appears in 13th century FRENCH Arthuriana as the foster mother of Lancelot. Attempts have been made to link her to Celtic mythology but not conclusively, and these Celtic candidates could just as easily have been conflated with her after the fact. Her connection to Excalibur comes post-vulgate.
Camelot can be identified with Camulodunum, the capital of Roman Britain (now Winchester), or Camalet, also known as Cadbury Castle, an iron age Celtic hill fort.
Arthur was not stolen from the Welsh because he never exclusively belonged to them in the first place. He belonged to all Celtic Britons, including the Cornish and Bretons, as well. Through the Bretonic tradition, he was introduced to the French, who were primarily responsible for creating the version of Arthurian legends most familiar to us today, not the English. The familiar forms of Guinevere, Bedivere, Gawain, etc are French, not English. The most famous English version of Arthur comes from Sir Thomas Mallory, who primarily sourced from the French tales.
It is the nature of myths to evolve, and there never will be a “true” version.