Why does it say I am not eligible for electronic filing because my NY state tax return claims a solar and wind energy credit carryover?

The State of New York determines whether your return can be e-filed based on the schedules and forms included with it.  They must have determined that the carryover you mention precludes your return from being e-filed.

Still....I'd wait until 10 Feb and to check again then before deciding to mail file.

Sometimes a weekly update will finalize in some background form that is all that is needed to allow it to be e-filed.  Sofware updates typically happen on Wed or Thurs evenings, so Fridays are the best time to recheck whether hang-ups are cleared.

IF not then, whether you want to try another week later is up to you.....or just go ahead and print and mail-file.