"The modern Welsh language is descended from the languages of these Celtic people. But the Celts had not lived in Britain for long, either."

"either" in this sentence indicates there's a similarity or connection with something mentioned previously. See entry #5 https://www.collinsdictionary.com/dictionary/english/either It's used in negative statements.

In this case, I think it's linking how the Saxons weren't the original inhabitants and neither were the Celts. You probably should have also copied a couple previous sentences to make it clearer. I'm assuming the text had mentioned something about the Saxons being the most recent arrivals or not being present in Britain for very long.

"either" used like this is sort of like a negative version of "too".

Examples

"The Saxons haven't lived in Britain for very long. Before the Saxons, the Celts lived here. But the Celts had not lived in Britain for long either."

compare that to a positive statement

"The Saxons brought their language to Britain. Before the Saxons, the Celts lived here. The Celts had their own unique language too"

"Jack didn't go to the party. Sally didn't go either."

"Jack was at the party. Sally was there too."

"Jack doesn't have a car. Sally doesn't have one either."

"Jack is tall. His sister Sally is tall too."