Some real estate websites who want to sell houses in our country to rich "expats" saying that the town is full of this colour because of its "Mediterranean essence" and because it's "a fishermen's town" and things relating it to the sea. That is not the case, it's true that cultures in the Mediterranean region use this pigment, but it's not associated to the sea and it does not appear more often in coastal areas. You'll find just as many examples in the inland, if not more. Those claims are just a way to exoticize the coast and sell it with the words that these rich foreign people want to hear for their Mediterranean fantasy, disregarding the truth about the local culture.

That's what foreigners or people selling things to foreigners have to say. Now let's look at another possible mistake repeated in many local websites.

They claim that this colour was invented for the first time in the year 1704 by a Prussian man named Heinrich Diesbach. For this reason, this colour is also known as "Prussian blue". According to these websites, he would have been the first person to start using cobalt to make blue, claiming that before him the colour blue had to be made with the very expensive lapislatzuli, thus blue was extremely expensive before 1704. This is not only false, but shows a tremendous ignorance of Early Modern archaeology, because the vast majority of table pottery in the 1600s and early 1700s Catalan Countries and other parts of Europe was blue made with cobalt oxide. Cobalt blue was a very widespread pigment combination since the 1500s, and already present in this part of Europe since the 1400s!

Exhibition of pottery found in the archaeological site of El Born in Barcelona, Catalonia. The site was demolished and covered up in the year 1717, but most of the pottery is from the 1600s. These are examples of what is called "Catalan blue ceramics".

You might also have heard of Delft blue pottery, made in the Dutch city of Delft in the 1600s and 1700s, often with motifs inspired by Chinese porcelain (though Delftware is not porcelain). That's also blue made with cobalt.

Heinrich Diesbach might have made a synthetic pigment mixing different materials (including cobalt oxide) and industrially produced it to sell. But cobalt oxide had been known and used for centuries. It was pioneered in the Middle Ages in modern-day Iraq. It became very popular because the Persians sold the pigment to the Chinese (in China known as "Muslim blue"), where it was used to make the famous Chinese porcelain (which was very popular throughout Asia and to a lesser extent parts of Africa and Europe, in the Early Modern period it would also become very popular in Europe). Through the Arabs, it reached Southern Europe, where it became very popular, and in Catalonia it ended up becoming the single most popular colour for pottery for a while.

Left: the David Vases, an example of Chinese pottery using cobalt to make blue. Made in Yuan dynasty China in the year 1365. Middle: an example of Iznik (Turkey) pottery from the Archaeological Museum of Istanbul. Made around 1480. Right: vase made in Italy around the year 1520. Sèvres Museum.

I don't know how long it has been used to paint walls, but we can definitely find it in many European tiles since the 1400s reaching a lot of popularity in the 1600s-1700s including among the artisan class (lower class). Blue pigment would by no means have been unknown nor limited to the expensive lapislazzuli in Southern Europe before 1706.

I have found this short documentary by an anthropologist about how this blue colour was used in Vall-de-roures (La Franja) to paint the walls and whiten clothes. The industrially-made pigment that was comercialized to paint walls and wash clothes with until recently was still made of cobalt, as explained by this anthropologist. So, as pointed out in the comments, it can't be Diesbach's invention, because Prussian blue's novelty was the very fact that it doesn't use cobalt.

So, as far as I know, there is no evidence to claim that the use of blauet in whitewashing walls comes from Diesbach's commercialized combination, or that it was not done before Diesbach's invention.

But it's hard to say when it started. I haven't found much research about blauet's historical origins. Searching for it is also made difficult by the fact that the word blauet in Catalan is also the name of one of the most colourful birds of our country: the kingfisher. And there's many people talking about this bird, he's definitely a popular guy!