You’re using the right document (the Related Article, linked above) to perform this transition.
If the telephone number you have within a country or region is not accepted by the Apple prompts, contact Apple Support and discuss this with them.
The + is used to indicate the position for the international dialing prefix in the telephone number, and will be followed by the country code. The international dialing prefix is not part of the telephone number, and this prefix is specific to the caller of the number. If whatever you’re entering won’t take the +, don’t enter it.
Telephone numbers are not particularly consistent even within a country or region, with some telephone providers requiring more or less digits or prefixes. In the US (and the North American Numbering Plan used in the US and a number of paces in North America) for instance, some telephone providers require ten-digit dialing, and some others permit or sometimes even require fewer digits.
Yes, phone numbers are a mess. They’re much better than they were years ago. It wasn’t that long ago that you could not dial internationally, and had to call an international operator (00, in the US) for that. But they’re still inconsistent and confusing.