The language is slightly different in the two sections of the Administration Guide that you’ve referenced in this question. In the “Planning” section the reference reads: “The default page group, 0, allows you to use up to 16,777,214 database pages containing up to 255 records/rows per page “
In the “Area” syntax we see a few references, all similar to this: “Specifies the initial number of pages to be included in the area. Primary-page-count must be an integer in the range 2 through the maximum number of pages determined by the MAXIMUM RECORDS clause of the SEGMENT statement. The upper limit is 1,073,741,821. “
Note that the difference in these descriptions is that the first one specifically says “16,777,214 database pages containing up to 255 records/rows per page” while the latter references the MAXIMUM RECORDS clause. So the reference to a maximum of 16,777,214 pages is accurate when the MAXIMUM RECORDS clause is set to 255, which is the default. In essence, the maximum number of pages for an area depends on the MAXIMUM RECORDS PER PAGE specification on the SEGMENT.
This specification can change the internal format of the DBKEY, as far as how many bits are used for page number and how many for the Line number (also called the radix).
The default is MAXIMUM RECORDS PER PAGE 255, which results in a "standard" dbkey format (24 bits for page number, 8 bits for Line Number)
For the default MAXIMUM RECORDS PER PAGE 255, the maximum number of pages is 16,777,214.
If you defined MAXIMUM RECORDS PER PAGE 3, the maximum number of pages would be 1,073,741,822.
We do not recommend using anything but the default unless there is a very special condition requiring it.
With the introduction of PAGE GROUPs (also specified at the SEGMENT level) there has not really been a need for customers to use a non-standard radix to get more pages for a database.
In the same manual, in the section with the syntax for SEGMENT statements, there is a “Usage” section. This contains a table that shows the maximum allowable page number for each different value of the MAXIMUM RECORDS PER PAGE specification in the segment definition.