The Tool I Use
First off, and potentially important, I do a lot of my game prep in an online directory. In particular I use Google Drive and the google apps suite for most of my game prep but that is less important than that I use an online directory. This lets me work on my session prep on break at work, at home, on the road, and wherever else I may be provided I have time and access to the internet. Not that I am always working on my game, but if I'm away on a trip but will be home in time for game, it is always good to be able to do game prep on the road without having to make special considerations to make it happen.
Also, I have access to my notes online when running game which means I don't have to print everything off which saves me time and space.
The top of my session prep notes is a recap section. Here I do 4 bullet points, and I try to pick 4 stand out moments that happened in the previous game. Often times these are important plot points, but they can also be fun or silly moments that stick out. The idea with the recap points isn't to do a whole rehash of the session, but to trigger both my and the players' memories of what happened. I find with me - and with others - that once you get them to start accessing some memories of a past session, the rest will come pretty fast. By sparking a memory with the big moments - be they important, silly, or just awesome - is a good way to do that.
After my recap I leave myself a section for the current situation. The first paragraph here is the basic situation. I try to keep this brief, and never more than a paragraph. The second paragraph will mention any important characters that are involved but didn't warrant mention in the previous paragraph. The third paragraph is what the PCs plan to do. Effectively, it looks something like this:
The PCs are guests in the Sini Palace. They await the arrival of Selby Atterton who can vouch for their identity and word. They've been 'gifted' a suite of rooms under heavy guard in the East Wing.
The Queen's Bodyguard, Estelle Fulton, is keeping a close eye on the PCs. Captain Alvard recognized Robert from the war and smoothed things out.
The PCs intend to ask Queen Victoria Sini with help with problems to the South West. They have copies of the treaties from the war in Pedor. They are also calling in a favor owed to them from previous work.
Just a few sentences for each, and I have what I need for where they are. That first scene then lets the PCs come to decision points for what they want to do.
Potential Future Encounters & Scenes
From there the rest of my notes are broken down into the next potential encounters and scenes. If the PCs are on a quest, this would be the next few major beats or things around those. For example, it could be places and ways they can find information on where something is, and what they'll find there if the PCs are still looking for that. Alternatively, it could be about the environment they'll see on the way, and what they'll find when they arrive. Along with any notes I may need for inside, or what comes after.
I try to have more than I'll need for a session in case the PCs find a way to skip something, or to clear something faster than expected. Normally this isn't hard. A few times it has been life saving.
Islands of Information, Not The Road
One key thing, the stuff I prep are islands of information not the whole path. I don't write up how I expect the PCs to get from A to B, nor do I expect them to go from A to B. If the PCs need to get the quest from A, then collect 3 pieces of information before going on to the main body of the quest then I will have all those noted down, but I won't have it down for an order or cause and effect. Those things I do live.
If the PCs want to skip getting the info and just try to get into the location they can. If they fail, they can always go back. If they have a good idea? We can move forward. Nothing is so fleshed out I'm married to how it has to happen. Instead I sketch out enough I have a good idea of what is going on and how things could go.
The more you have things defined, the more you're going to want to - consciously or subconsciously - make it happen that way and the more agency you take from your PCs. Instead just provide yourself the info you need to make a decision in the moment, and let the PCs decide how things happen.