A GPS-based navigation app like OS Maps does not need a cellular network connection to function once maps are downloaded [Do it the evening before the day you set off as part of your equipment checklisting]. GPS itself works independently of cellular data, relying on signals only from GPS satellites. The phone uses these signals to determine your location, and if you have downloaded maps beforehand, the app can use the stored data for navigation without a cellular connection.
Dedicated GPS devices like Garmin are said to be designed for accuracy in challenging conditions, i.e. where getting a satellite ‘fix’ is difficult - like in tall dense forests and below & between high-rise buildings (neither of which are on my SOTA routes). Whenever I test the accuracy of my phone’s GPS by zooming in the display to maximum whilst standing next to an unambiguous feature in the landscape, the GPS spot is, ahem, spot on.
This is way more accurate than the traditional method ‘I grew up on’ of finding your position on a map by taking bearings of at least two known landmarks and plotting them on the map. Depending on various factors this is usually within 100m, which is fine for most navigation especially if there are features on the map you can confirm are nearby.
And actually, in most of the UK there are usually so many landscape features (stonewalls, crags, farm buildings, etc) marked on the OS 1:25k paper map you can often navigate the entire route without using a compass.
Garmin claims a position accuracy within 3-5m under normal conditions. Apparently, iPhone’s GPS position accuracy is also 3-5m in open areas with clear visibility to satellites. However, in urban environments or indoors, accuracy might decrease due to signal blockage or reliance on Wi-Fi and cellular triangulation, potentially reaching 10-30m.
Re the previously-mentioned advice from Scottish Mountain Rescue, it does not favour dedicated GPS devices over smartphones.
https://www.scottishmountainrescue.org/mountain-safety-advice/
“Always, always have a map and compass and know how to use it. Smartphones or GPS are excellent navigation aids but should not be relied on solely.”