UK.
Until recently, if I wanted an appointment I had to phone the GP surgery the moment it opened at 8:30 in the morning, wait in a phone queue for ten minutes or so before I got to speak to a receptionist who'd give me an appointment with which ever GP had some free time that day. It wasn't usually possible to book an appointment several days in advance.
A couple of months back they switched to an app which gives much more flexibility, allows you to choose which doctor you want to see and allows you to book appointments in advance. I do worry that they're going to push everyone to use that since old gippers are likely to struggle with the app unless they're semi-tech savvy. Also, it's obvious to me that they're setting this up to use AI to triage requests if they're not already doing that.
Appointments always used to be face to face but since covid they're increasingly phone consultations especially for follow-ups. If it's a first, diagnostic appointment it's still likely to be face to face though.
For face to face, the wait time is generally less than half an hour from the point I get to the GP surgery.
Obv. it's free at the point of use. I've paid my taxes.
Edit to add: if you're on low income, or are a child, old, etc you get your prescriptions free. Otherwise you have to pay for them at £9.90 per 2 month prescription. I'm on a shitload of medication and that would normally cost me well over £500 a year, but I get a prepayment certificate which costs me £114.50 a year and covers all medication.
My GP surgery was the same (except 8:30 not 8:00), but moved to an app a couple of months ago. Given that I suspect the point of it is to allow an AI to triage appointment requests I wouldn't be surprised if yours 'upgrades' as well.