Old English had a variety of grammatical suffixes; nouns, for example, had case suffixes. The word for ‘stone’, stān, for example, could appear as...

stān  (subject or object, singular)
stānes (possessive singular)
stane (dative singular)
stānas (subject/object plural)
stāna. (Possessive pl.)
stānum (dative plural.

Those suffixes were in unstressed locations, and by late old English the system had started to fall apart. One thing lost was the distinction between short /a/, short /u/, and short /e/ in the suffix. What was left was a bit schwa-like, but was typically written with an ‘e’. So, we get ...

stān  (subject or object, singular)
stānes (possessive singular)
stane (dative singular)
stānes. (subject/object plural)
stāne. (Possessive pl.)
stānem (dative plural.

Note that the distinctions in the system have reduced. The singular possessive now sounds like the nom. Plural. The next phase dropped a couple of sounds:

stān  (subject or object, singular)
stānes (possessive singular)
stane (dative singular)
stānes. (subject/object plural)
stāne. (Possessive pl.)
stāne. (Dative)

Now we’re down to just three forms: stán for sg subject/object, stánes for sg possessive but also nominative plurals, and stáne for everything else.

So one source for a lot of those e’s is case suffixes that were still pronounced in much of Middle English. This is particularly likely if the word is in an indirect object or a possessive plural . Spelling wasn’t particularly regulated, and humans are humans, so a number of scribal errors crept in too, as well as people creating analogical spellings. Eventually, -e suffixes faded from pronunciation, but we still write a lot of them b/c the affect the preceding vowel

This info here is mostly from Baugh & Cable’s A History of the English Language.