Are the Basques and their language the last remnants of Atlantis from further south on the Iberian peninsula?

According to this site, yes.
Many people left Atlantis before it sank. The Basques believe they are descendants of Atlanteans.
https://www.theatlantisproject.org/basques/
While observing and studying a group of linguistically interrelated Indian tribes along the Amazon River, archaeologist Marcel Homet learned that their common language, Tupi-Guarani, contains idioms that are strikingly similar to the Basque language. Edgar Cayce says the ancestors of the Basques were Atlanteans who moved to the Pyrenees Mountains of southwestern Europe.
https://eraoflight.com/2017/08/18/edgar-cayce-on-the-descendants-of-atlantis-and-rh-negative-blood-type/

There are other, possibly more likely explanations for the uniqueness of the Basque language and culture.

https://en.wikipedia.org/wiki/Basques
The Basque language is thought to be a genetic language isolate. Thus Basque contrasts with other European languages, almost all of which belong to the broad Indo-European language family. Another peculiarity of Basque is that it has been spoken continuously in situ, in and around its present territorial location, for longer than other modern European languages, which have all been introduced in historical or prehistorical times through population migrations or other processes of cultural transmission.

https://en.wikipedia.org/wiki/Basque_language
The impossibility of linking Basque with its Indo-European neighbors in Europe has inspired many scholars to search for its possible relatives elsewhere. Besides many pseudoscientific comparisons, the appearance of long-range linguistics gave rise to several attempts to connect Basque with geographically very distant language families. All hypotheses on the origin of Basque are controversial, and the suggested evidence is not generally accepted by most linguists.