What is the canon for the creation of Anauroch?

According to Netheril: Empire of Magic boxed set (TSR 1147, published in 1995), what is currently the desert Anauroch used to be lush lands 5000 years ago. Those were the lands where seven fishing villages first formed a kingdom (-3859 DR), named after the king Nether the Elder (and his successor, Nether the Younger).

In time, the kingdom discovered the so-called nether scrolls, which allowed its citizens to master magic quickly. Within the ninth century of the foundation of the Netherese kingdom, they had already managed to create the first floating cities. They kept on expanding and started wielding immense power.

Into their fourth millennia, an outcast named Olostin came across a strange cone-like being, a member of the race phaerimm. After information gained from Olostin, the phaerimm starting casting "magic drain" spells in the year 3398 (-461 DR). These had devastating effects:

The permanent magic drain spells began draining life energies as well, slowly killing everything within their sphere of effect. ... Fortunately for the Netherese, the effects of the magic drain spell were visible. Near the largest flying cities, the land slowly began turning into a sandy desert. At first, ... they simply flew the city (sic) to a different place. As the “land’s plague” continued to follow the cities, however, the archwizards knew something was wrong. But in moving the cities around, they helped establish the borders of the desert that would one day be known as Anauroch.

Some three centuries after the fall of the empire, which was caused by the attempt of one overambitious archwizard, Karsus, to become a god, the spread of the desert had stopped. It is not clear why, but it is possible that the sharn, a race of beings who are enemies of the phaerimm, might have played a role. (This is confirmed in the sourcebook Lost Empires of Faerun, published in 2005.)

What is the canon for the disappearance of Anauroch?

According the Forgotten Realms Campaign Setting (published in 2001), the City of Shade, one floating Netherese city that had disappeared into the plane of shadows right before Karsus's folly, reappeared over the skies of Faerun in 1372 DR.

We learn from the Forgotten Realms Campaign Guide (published in 2008), within a century of their return, the Netherese had struck hard on the phaerimm, and the desert was reclaimed:

Rivers now flow from the melting glaciers, rain falls, temperatures are moderate, and in some places vegetation is particularly lush. Netheril is a land reborn, despite its cruel overlords.

It appears this is the current (Feb 18, 2018) status of the Anauroch entry at the FR wikia.

What is the canon for the recreation of Anauroch?

Finally in 1487 DR, the City of Shade falls on top of Myth Drannor; as we read in the Sword Coast Adventurer's Guide (published in 2015, page 18). This causes the destruction of both cities. A year after, a battle in the Netherese lands awakens a hive of phaerimm, and they use life and magic-draining power of the so-called Memory Spire causing the desert to come back.

While the first desertification of Anauroch was a very long process taking centuries, the second time it seems to have happened in a manner of years. But it has indeed become a desert, as mentioned multiple times in the SCAG:

Flying Netherese cities ... hung high over a verdant land that is now the desert of Anauroch. [page 48]

Delzoun ... stretched from the western edge of what was then the Narrow Sea (later, the Great Desert of Anauroch) west almost to present-day Silverymoon, ... [page 59]

Evereska ... to the east lies the hungry desert sands of Anauroch. [page 82]

Conclusion

There are no conflicts between the past official material and the information provided in the SCAG. It is just that the creation of the desert has happened twice.

The 5e Espruar alphabet is from past editions - it's 3e that's different!

As KRyan's answer notes, the elven alphabet in the 5e PHB is not and is not meant to be Espruar. However, the Thorass and Espruar alphabets given in the 5e Sword Coast Adventurer's Guide do differ significantly from the versions presented in the 3e Forgotten Realms Campaign Setting - they are actually using the same characters from the original versions of those alphabets as presented on page 8 of the 1e Forgotten Realms Campaign Setting box set handbook, Cyclopedia of the Realms:

Thorass and Espruar were dramatically redesigned in the 3e FRCS with no in-universe or, so far as I can tell, out-of-universe explanation given. From googling around to investigate, reception seemed a bit mixed; some people think the redesigned script was much better, others preferred the original version.

It is not clear why 5e has returned to the original version of Thorass and Espruar in SCAG, and whether that choice was deliberate or not (both versions of Espruar come up pretty readily if you google for it, so whoever was responsible for those images might have just picked one at random!) If it was deliberate, I would hazard a guess that it is because 5e made a big deal about returning to D&D's roots and trying to restore appeal to old 1e and 2e players, and the decision to use the classic FR alphabets plays into that.

Whatever the out of universe explanation is, I cannot find any evidence that a change in script has been noted in-universe, so one assumes that these changes must be considered retcons. If you're dead-set on a canonical explanation, I'd just chalk it down as another bizarre consequence of all the magical shenanigans that accompany every edition change.