When on a big long run or fastpack in the mountains or backcountry, here are some different ways I find my way around.
In an area with well-established and signed trails, I often carry a 1-page paper overview map, a paper cue sheet, and my GPS watch. My cue sheet tells me which way to turn, at what mileage (approximately). Usually this is enough - I can just look at the sign, cross reference it with my cue sheet, and make the right choice. Sometimes glancing at the map is handy for context.
This can be accomplished with a GPS app on my phone, but I find it's usually quicker to pull out the paper.
I usually use a single sheet of paper with a map on one side and cue sheet on the other. I can also mark water sources and other points on the map.
I print out my maps from CalTopo.
In these situations, you need to know exactly where you are. You don't want to be bushwhacking 50 yards away from the trail. This is where having a GPS track on my phone is helpful. Since I have a Garmin Inreach Mini, I use the Garmin Explore app on my phone. I can upload a GPS track to the app, ensure it and the relevant map layers are downloaded to my phone, and then head outside. When necessary I'll pull the phone out and check if I'm on track, and see what's coming up.
The Caltopo app is made for this as well. I use Caltopo on the desktop for route planning, but would need a subscription to cache maps on my phone (and since I have the Garmin subscription anyway, I am not bothering to get a Caltopo subscription as well).
This usually applies to off-trail navigation:
A phone app does work for this, but it can be clunky - you have to find the right zoom level to give you the detail you need, but also enough context for the larger area. Again, I find it easier to pull out a piece of paper to consult. I use a paper topo map and sometimes a compass to get myself pointed in the direction I need to go. It's useful to know how to orient a map and take a bearing: How to Use a Compass || REI - YouTube