The song has two names, which are 1) Remember and 2) Zelda's Wish
I have not found a piano arrangement for both of them.
Remember
Zelda's Wish
This is on site under the title "Captured Memories" (though I could have sworn I took that title from the channel that uploaded the first video you linked...)
https://www.ninsheetmusic.org/browse/series/TheLegendofZelda#sheet3545 (https://www.ninsheetmusic.org/browse/series/TheLegendofZelda#sheet3545)
Yooo thank you so much!
I swear that I've never heard that title before... in the OST tracklist, it's called Zelda's wish.
Why is it called captured memories?
What OST tracklist are you using? I've yet to see a definitive listing - off the top of my head all the ones out there are either incomplete or unofficially translated, without one naming system in widespread use.
The version I have downloaded has it listed as Captured Memories (but I don't remember where I downloaded it from...)
Chatted over Discord and the Japanese OST translates to "Zelda's Wish":
https://zelda.gamepedia.com/The_Legend_of_Zelda:_Breath_of_the_Wild_Original_Soundtrack#PLAYBUTTON_.22The_Legend_of_Zelda_Field_Music_Collection.22
https://columbia.jp/prod-info/COCX-40313-7/
https://tower.jp/item/4696693
I'll update the sheet accordingly when I get a chance. Thanks!