Wasn't he a reincarnation of prince Shoutoku?
no... according to Tsukasa, Nasa's a bit more handsome than Shoutoku

But in all seriousness, it seems like Nasa really is just a normal boy. I think I remember his grandpa meeting Tsukasa post-war but that's about when it comes to his pedigree.
To be honest, I think he must be connected to Shotoku, since Nasa actually recalled a memory of
Shotoku's at some point in his dreams. He thought it was related to the time he visited Nara and the Horyu-ji temple, since it was a memory from when Shotoku was out front of said temple and seeing Tsukasa off as she went to China/Sui as part of an envoy.
This happened in
Ch.120, in case you want to check yourself. For reference, 'Miko-sama' is one of the names that Shotoku has gone by. Another figure mentioned in the memory is
Ono no Imoko, who worked with Shotoku as envoy to the nation of Sui. In other words, the context is very strong to imply Nasa was recalling a memory of Shotoku's in that instance, somehow.
Also... The kid here is
Sugawara no Michizane at 5 years old, pretty sure. Note Michizane's listed years of life in that wikipedia entry, and note he'd be 5 years old in 850 when most of this chapter takes place, and that he went on to earn that title of 'God of Learning' that the kid is proclaiming so proudly about.
For reference, the last time Michizane actually appeared in the manga was back during the Kaguya-Emperor romance backstory arc, specifically in
Ch.204. At that time, stated to be 891, he would be about 46 years old, and about 12 years from his own death in 903. Later, during the arc about Nasa's grandfather, Tsukasa has a couple flashbacks intermixed with modern day scenes during
Ch.216, where the first one mentions Michizane's reputation (he was disgraced and exiled leading up to his death, and only later deified as the god of learning).