In the GNU project, man pages are secondary. It is not necessary or expected for every GNU program to have a man page, but some of them do. It’s your choice whether to include a man page in your program.
When you make this decision, consider that supporting a man page requires continual effort each time the program is changed. The time you spend on the man page is time taken away from more useful work.
For a simple program which changes little, updating the man page may be a small job. Then there is little reason not to include a man page, if you have one.
For a large program that changes a great deal, updating a man page may be a substantial burden. If a user offers to donate a man page, you may find this gift costly to accept. It may be better to refuse the man page unless the same person agrees to take full responsibility for maintaining it—so that you can wash your hands of it entirely. If this volunteer later ceases to do the job, then don’t feel obliged to pick it up yourself; it may be better to withdraw the man page from the distribution until someone else agrees to update it.
When a program changes only a little, you may feel that the discrepancies are small enough that the man page remains useful without updating. If so, put a prominent note near the beginning of the man page stating that you don’t maintain it and that the Texinfo manual is more authoritative. The note should say how to access the Texinfo documentation.
Be sure that man pages include a copyright statement and free license. The simple all-permissive license is appropriate for simple man pages (see License Notices for Other Files in Information for GNU Maintainers).
For long man pages, with enough explanation and documentation that they can be considered true manuals, use the GFDL (see License for Manuals).
Finally, the GNU help2man program (https://www.gnu.org/software/help2man/) is one way to automate generation of a man page, in this case from --help output. This is sufficient in many cases.