@AlexEliot
You’ll note that definition of unit is informal, and that I already said such exceptions exist. The way unit is used
in the definition of cavalry that you linked is obviously not meant to be the informal usage. End of the day, in a military context “unit” does not refer to a single person (even the informal example you use doesn’t refer to individual soldiers, but individual tanks, each of which would be crewed by multiple soldiers).
Yes, unit is a word with multiple definitions. But the context in which that word is used tells us which definition we're meant to be using - we can't simply define words as we wish when other people are the ones using them. When reading the dictionary definition of a word, I'm going to assume the dictionary is using formal language. Hence when the word "unit" appears in the definition of the word cavalry, I'm going to assume the dictionary is using the formal definition of unit, and not the informal one (which the same dictionary lists as the
sixth definition in unit's own entry, which should tell you a few things).
You also seem to be confused as to what I mean by individual soldier. A cavalryman would not describe himself as "a cavalry." https://en.wikipedia.org/wiki/Cavalry lists several ways to refer to a single cavalryman. But
500 individual cavalrymen would be
500 cavalry. I don't know if your confusion was willful or not, but hopefully this post clarifies.
As I said before, when referring to the number of cavalry that a specific army has, cavalry is an uncountable/mass noun. From https://en.wikipedia.org/wiki/Mass_noun - regardless of how many of them there are, they are always "treated as an undifferentiated unit, rather than as something with discrete elements" (in this case a "discrete element" would be an individual soldier). For example, no matter how many pieces of advice you give someone, they are collectively referred to as advice - not advices. An no matter how many chairs you have, together they are furniture, not furnitures. Sometimes an uncountable noun can be countable in certain contexts (“a school of fish” vs “schools of fishes”), but this isn’t one of those cases. A group of cavalrymen are cavalry, not cavalries. If your army has 500 cavalrymen, you have 500 cavalry.
Here's some examples of what I'm talking about. From https://en.wikipedia.org/wiki/Battle_of_Waterloo (emphasis added):
"The French army of around 69,000 consisted of 48,000 infantry,
14,000 cavalry, and 7,000 artillery with 250 guns." Saying the French army has 14,000 cavalry means they have 14,000 individual soldiers who fight on horseback. They do not have 14,000 cavalries, as your usage would suggest.
"The French army formed on the slopes of another ridge to the south. Napoleon could not see Wellington's positions, so he drew his forces up symmetrically about the Brussels road. On the right was I Corps under d'Erlon with 16,000 infantry and
1,500 cavalry, plus a cavalry reserve of 4,700. On the left was II Corps under Reille with 13,000 infantry, and
1,300 cavalry, and a cavalry reserve of 4,600. In the centre about the road south of the inn La Belle Alliance were a reserve including Lobau's VI Corps with 6,000 men, the 13,000 infantry of the Imperial Guard, and a cavalry reserve of 2,000." The same as above. If I Corps has 1,500 horsemen, then I Corps has 1,500 cavalry, not cavalries. If II Corps has 1,300 cavalrymen, they have 1,300 cavalry, not cavalries.
"Bodies of infantry
and cavalry were pouring down on us," - Once again, it is not "Bodies of infantries and cavalries," but "Bodies of infantry and cavalry." Both infantry and cavalry are uncountable.
In all of these cases, the text is describing a number of individual cavalrymen. And in all of these cases, "cavalry" is treated as an uncountable noun. This is what Wiktionary's first definition of cavalry is referring to, and is the way you should be using it as well.