For me, what doesn't make sense is that the game works perfectly in the tests and when exporting it has this type of problem when saving.
No, this happens often and I've seen it many times in other people's projects! For example: you save something in Local Storage and immediately switch to another layout. On start of that other layout you read the same data from Local Storage. This may work in preview, but will fail in an exported game or on a slightly slower PC, because LS operations are asynchronous. The write request may not be completed before the read request, and the data in LS may become overwritten with default values.
That's why I'm asking you to share the complete screenshots of all relevant events, or a project file.