When I was looking at the plural noun ending for English, it said that it came from the Proto-Indo-European suffix *-es. I looked at the Spanish etymology. It didn't give much information except that it came from the Latin -es for 3rd declension. I have a feeling that they might be, but I'm not sure.
It's (probably) a true cognate!
Back in Proto-Indo-European times, noun endings indicated case as well as number: there was no single specific "plural ending", but there were various endings used for different cases in the plural. The accusative "feminine" one is reconstructed as *-eh₂-ns (though it's unclear if the feminine was actually a distinct category in PIE or if that happened later).
In Latin, this eventually became the first-declension accusative plural ending -ās, which shows up in Spanish words like aguas < Latin aquās.
In Old English, this eventually became the A-stem accusative plural ending -as, used for the most common class of nouns. Eventually this got generalized to (almost) all nouns, giving Modern English -(e)s.
(The -s that shows up in Spanish words like manos and hombres is related, too, it's just less obvious in the other declensions.)