Can you explain why you think that "1" should be replaced by "One" ?

That's the correct title. https://www.detectiveconanworld.com/wiki/The_Black_Organization:_One_Billion_Yen_Robbery_Case

Depending of the sources, I have either "The Black Organization: 1 Billion Yen Robbery Case" or "The Black Organization: One Billion Yen Robbery Case" ?

The Black Organization: 1 Billion Yen Robbery Case :

• https://myanimelist.net/anime/235/Detective_Conan/episode/128
• https://en.wikipedia.org/wiki/List_of_Case_Closed_episodes_(seasons_1%E2%80%9315)

The Black Organization: One Billion Yen Robbery Case :

• https://anidb.net/episode/25867
• https://www.detectiveconanworld.com/wiki/The_Black_Organization:_One_Billion_Yen_Robbery_Case (your link)

So, do you have a proof of the title used for the first official release of this episode in an English speaking country ?

Neither is correct, it's never been released in an english-speaking country. And it's better to spell it out since it could mistakenly be read as The Black Organization (Part) 1: Billion Yen Robbery Case.

Also https://7esl.com/when-to-spell-out-numbers/

No the platform standard of writing rules are needed to use. So number (1 never one, but "one" are lucrative) are required. Crunchyroll have actually not that episode, so we can't check them. But wait till the episode present on Crunchyroll on spring 2023.