We probably should decide how much conflict we want to imagine happening here lol.
Wars from the 1700s-1800s (a couple hundred years ago from today) just aren't thought about much during my regular daily life, but none of those were global catastrophes right.
So if we can manage to avoid major nuclear destruction, then it could be pretty tame after 300 years!
Assuming we don't all destroy each other, then we mostly keep our knowledge base, so we don't need to restart from a basic agrarian culture lol. Someone saved wikipedia right??
There will still be an unbelievable amount of losses from starvation alone, so we're definitely restarting the population from small communities.
But 300 years of repopulation, and 300 years battery research might actually get us to something approaching the early 1900s again! (Around the 1930s is when about half of American households had electricity.) Cities are possible, we start getting back into shipping between countries or continents. If we add internet into this mix, we get even further!
Honestly, if we're talking about hundreds of years (and humans don't self-destruct) then I actually think we don't get set back too far on the grand scheme of things lol.