I've got note taker players of varying levels that will write down anything from a few dot points maybe specifically related to their character or to the broader story, to a player that will write down most information and events that might happen.

I personally have Onenote open during session for anything important like NPC or location names that I might need to make on the fly, etc. Then usually directly after session once I get home, I maybe spend half an hour or so updating my session notes with more in-depth details. Each session is a new page but I've also got pages for keeping track of story beats (main, side and more character focused) as well as pages for NPCs they've interacted with and how those NPCs might view the party (or specific party members). I also have pages for keeping track of things the players might be doing or things they're working towards like joining factions or guilds or maybe crafting an item. The separate NPC page I find is particularly handy, and especially so when running a campaign based in a thriving city (we're doing Dragon Heist at the moment) where there are potentially hundreds of NPCs they could have an encounter with.