I’ve had two inplants under a local anesthetic. It was no worse than having a tooth extracted - both during the procedure and the discomfort afterwards.
If you want this done under sedation you’d need a find a dentist who would be willing to do this. If the one you consult doesn’t offer it, they may be able to recommend someone who does.
I don’t know about a GA, that has a risk so they are reluctant to do it . You also have to go into a private hospital so I’d imagine it will be very expensive.
Remember it’s a multi stage procedure that takes months. They have to assess you to see if you are suitable, they won’t do it if you smoke or have gum disease or your dental hygiene is poor or you have certain medical conditions.
Then they need to check that you have enough bone for the implant ( the screw thing that goes into your bone ) to go into and sometimes they have to supplement it. Then they wait months .
Then they put in the implant itself . A week later they take out the stiches. Then they wait months, that’s for your own bone to grow round it and make sure it’s secure.
Then you go back and they take impression and a week or so later they fit the crown ( the white bit that looks like a tooth ).
So you will be back and forward for months. It’s worth it in the end but it takes a long time and it’s not cheap - perhaps about £ 3,000 per tooth . Maybe it’s a bit less of you have several done at once, I don’t know,
You will be a lot more £ id guess if you want sedation. I don’t know how it works if you need more than one at a time or how many they can do at once, I guess it depends where they are in your mouth.
that’s my patient version of what happens, I’m sure it’s not correct from a dental point of view.
Good luck.