Bambu Studio automatically fills this hole with supports but they are unnecessary and hard to remove. They dissapear when support/object xy distance is increased to more than 1mm. Is there a better way to fix this please?
Personally I mostly design supports into prints, or if not use manual supports to avoid this sort of issue.
Other ways around it are to use support blockers - to block it from adding support to the holes.
Painting support blockers unfortunately doesn’t work. It still puts supports there.
I understand - so you want to the flat surface above supported - but you don’t want the support structure to go through the holes.
I think I would just do a tiny support blocker above the holes on the bottom of the top surface and then not worry about that tiny bit not being supported - as the slicer should easily be able to bridge small unsupported portions.
It may or may not help but I rarely use support under things with 30 degree angles (the Bambu Studio default angle). That also happens to put support under threads causing the issues with removing. If I set the angle to even 29 degrees, the screw hole support disappears.
Since you want to support through those holes, if I understand correctly, I think it will just pull away from the threads and only have support in the clear part of the hole - I think.
YMMV though… Good luck!
Have also run into this issue and it led me to have to paint the supports on manually which fixed the problem for me. The only issue is that it only works on certain occasions when the section you’re painting has absolutely no connection with the section you’re trying to avoid. If the software somehow decides the section you want to avoid is part of what you painted it will put supports in the hole too. It’s very annoying.
This might work: Right-click on your model in Bambu Studio, then add a Support Blocker. You can make this larger or smaller to cover exactly the places where you don’t want supports.
I also tried to print the model anyway but those supports were very difficult to remove (had to use a drill). I will try Ukdavewood’s suggestion next.
I managed to solve it by covering the hole with one layer which I break with a screw as suggested by Ukdavewood. Tree supports are also a good solution but I had trouble removing them.
This really needs a print setting under support, “Maximum Unsupported Bridge Distance” I use M2.5 screws mostly and having to pick out those supports is a real pita.
Have you tried adjusting the angle for support? It can tune out some supports in screw holes depending on their orientation. Or can use self-tapping screws with plain holes?
I haven’t, because I’m not a fan of tuning. I’m not printing the threads, I just have tiny blind holes in the parts that I add support blockers to, when I remember. The problem comes in when you are iterating a part, you right click and select reload from disk. Then at some point the reload doesn’t work anymore (from splitting the parts) then you import again and forget. I know the overhang angle will help this, but to me it just seems logical that no printer will have an issue bridging 2-5mm gaps. I will try the support distance mentioned above, maybe I should start making my own profiles but that dropdown list of profiles becomes such a mess so quickly. And then I can never remember what changes I made for what reasons, the joys of old age I suppose.
This worked for my situation where I’m printing a dice with a void for a weight. Thanks!
Won’t be playing dice games with you! 
Another method that’s worked for me; select your model, right click and choose ‘Add part’. Then add a cylinder and size it smaller than screw hole on the x/y with a z height of 0.1. Now when you go to generate supports it will find a different route. Make sure to use tree supports.