Context options are not updated in the alias (back-end) when new value is either 0, FALSE or and empty string

Hello!

There appears to be a bug with exporting context options via hook_hosting_TASK_OBJECT_context_options().
Whenever I try to export a new value and the value is either 0, FALSE or an empty string - the back-end ignores the new value and keeps the old one.
So:
- if I have an option with a string value, say 'my value', and try to update it with '' (empty string) - it won't update.
- if I have an option with an int value, say 22, and try to update it with 0 - it won't update
- if I have an option with a boolean value, say TRUE, and try to update it with FALSE - it won't update

Spend half a day trying to figure out what is going on here.
May be not critical, but annoying and requires some workarounds.

If not to fix it, then at least to add a note to the hook_hosting_TASK_OBJECT_context_options() documentation.

Cheers!