In the series the name of the song A'Li played is "Pear Blossoms Turn White", but the original name I only found in Mandarin, with a translation for English:
墨雨云间 芳菲落尽梨花白
作词/于正崔轼ㄠ 作曲/工可刘灼
梁凡钱雷
编制/制谱 如鱼得森@虫虫钢琴
"Between the ink and rainy clouds, all the beauty is gone and the pear blossoms are white. "

As a musician, I focused on A'Li's music which I consider a treasure. But the other song you can find on YouTube (competition scene).

I'll put the link of the song A'Li played (solo) and the same song that she played with Shen Yu Rong. (flute). The song Jiang Li played in the guzhen was very hard to have. Nobody here found it, only that song sung by Mi Liang. It took me several days to find it. I had to search for it in Mandarin to come to the source.  I'll put here all the informations about this specific marvelous song.
Many people are asking about the song Jiang Li played in the guzhen. I'm a musician, I couldn't rest until I found him. After many days, I discovered all the information about this stunning song, including its sheet music.

In the first link you have the original song of the series (you won't find it in the playlist). In the second one you have  the song played by A'Li and Shen Yu Rong. In the third one, you have a musician playing that wonderful song on the guzhen. I'm going to put all the information about this song, so that if you want to play it (if you're a musician, like me). As you will see, I am putting the original title in Mandarin, as that is the source, with the English translation. In the fourth link you have all the informations about the song. In the fifth one you have the sheet music for piano (I'm playing it on piano and flute). In the 6th link you have all the songs of The Double. In my opinion, the best soundtrack I've heard this year. In the 7th link is the song sung by Mi Liang. Finally, the last one is the guqin version available on WJY's Weibo account and YouTube, a tribute especially prepared for those who loved A'Li's song.


●1-The original song of the series

https://m.youtube.com/watch?v=hQ1r37zJLL8

●2-A'Li and Shen Yu Rong playing

https://m.youtube.com/watch?v=luPFCptKc6M

●3-Musician playing the song Jiang Li played in the guzhen.

https://m.youtube.com/watch?si=-Mj65eWyZg7qo_-o&embeds_referring_euri=https%3A%2F%2Fwww.google.com%2Fsearch%3Fclient%3Dms-android-samsung-ss%26sca_esv%3D8fccc85c2f21a58f%26q%3DGuzheng%2B%2522Pear%2BBlossoms%2BTurn%2BWhite%2522%26udm&source_ve_path=MTY0OTksMjg2NjQsMTY0NTA2&feature=emb_share&v=hOo3Ej0npCI

●4-Complete informations about the song

墨雨云间 芳菲落尽梨花白
作词/于正崔轼ㄠ 作曲/工可刘灼
梁凡钱雷
编制/制谱 如鱼得森@虫虫钢琴
Between the ink and rainy clouds, all the beauty is gone and the pear blossoms are white. 
Lyricist/Yu Zheng Cui Shi 
Composer/Gong Ke Liu Zhuo Liang Fan Qian Lei 
Compiled/composed by Ruyu Desen@Chongchong Piano

●5-In this link you can get the sheet music for piano

https://www.gangqinpu.com/cchtml/1120439.htm

●6-In this link you have the complete soundtrack of the series. 

https://m.youtube.com/watch?v=7c3VEcDk180

●7-Mi Liang sings "When fragrance falls, pear blossoms turn white

https://m.youtube.com/watch?v=9v0qU-1HDj0

●8-Guqin version available on WJY's Weibo account and YouTube for those who loved A'Li's song. A beautiful tribute!

https://m.weibo.cn/u/1278603180#&video

https://m.youtube.com/watch?v=ZDXCP3fyOh8

Thanks for setting up the info here so it’s easier to find! As mentioned before, I’m looking around to get a flute to begin learning, is something like this suitable?

https://www.etsy.com/au/listing/1606830685/chinese-flute-hanfu-flute-hanfu-musical

I'm glad it's useful! You can start with the soprano recorder. German (wooden) flutes are great (Möeck). There are several models. If you need it, I can indicate the model for you. You can send inbox messages if that's better for you.