I know that for the most part, swords weren't necessarily the "first weapon of choice" for most soldiers (excluding the Romans) and were often more used as back up side arms in case something goes horribly wrong. I know that the Messer was used in Germany, but from what I hear, they were primarily used in civilian settings (as they were very sharp and thin, useful against no armor, useless against armor) but what about arming swords or bastard sword?
Regarding how swords were used, this previous question has answers by myself and u/PartyMoses about the user of swords in the Later Middle Ages and Early Modern period. These cover both military and civilian uses of swords. Please let me know if you have any follow-up questions.
Define "late medieval." Different people define the term differently, which could affect how people answer.
According to my understanding of the term (fourteenth century onward), this broadly coincides with the era of plate armor. For this, I suggest reading up on the German school of swordsmanship.
The primary sword at this time would have been the longsword (a two-handed weapon, the shortest of which are known as "bastard swords"). I have very little understanding of how swords were used, so I can't say much in terms of how they were used, but against armored opponents, multiple techniques that involve grabbing the blade existed.
Neither of the defining features of the messer necessitate such a blade (the defining features are that it's a single-edged sword without a full tang). Additionally, any sword's blade would have been useless against plate armor. As mentioned with the longsword, some of the main sword techniques against armored opponents were halfswording (grabbing the blade further up in order to guide it into a gap in the armor) and the mordhau (holding the blade with both hands and using the hilt as a hammer to the head).
For an example of a sword specifically designed for use against armored opponents, the estoc is a good thing to look at. It is essentially a longsword, but instead of a blade, there is a spike. The only effective way to fight a plate-armored opponent with a sword is to either thrust into a gap in the armor (as in the cases of the estoc and halfswording) or inflict blunt trauma (as in the case of the mordhau).