Both, actually!

So, there was probably a man named Taliesin, who was around in 6th century Wales. He probably wrote a few things that still exist, and was considered the founder of a lot of the genre. There is at least one mostly-contemporary reference to him, by a poet named Aneirin.

...But all of the subsequent references to him are at least three hundred years after he died, and his biographies start four hundredish years after his life, sometime around the root of the Culwich and Olwen story, which is also what twines him in with the King Arthur myth to start. From there, it grew and you can't always tell what was added in later with what really happened. I think a few of the later poems "attributed" to him may actually mention Arthur, as well. Plus a prophecies, a thing with a potion and being eaten and reborn, etc.

Also, there is the issue of translations and transcriptions. The written works were translated from older versions of the language, and how much was oral tradition and retellings mixed in before being written down much later is a question. (See: the debate on the Odyssey or many folk songs and oral history poems.) The upshot is that the oldest traceable copies of books where the "works of Taliesin" were written down are about ~1250, ~1382, ~1410, and the later bits of the sixteenth century.

As you can tell, someone probably did a lot of creative editing. Which means that we know someone probably wrote some of those works in the 6th century, probably named Taliesin, but anything else is very fun fable.

(Fun fact-- there is also the 13th century Thomas the Rhymer, who was a real person, and possibly wrote the English version of Sir Tristrem, but is also more famous for the romance turned folk song where he spends 7 years in Fairyland because he kissed their Queen. But Thomas the Rhymer is a fun song.)

https://d.lib.rochester.edu/camelot/theme/taliesin