These should be specified by the PCB place you’re planning to use.
As you have hinted at, the annular ring size needs to be bigger for internal layers to prevent “breakaway” (since the holes are drilled AFTER the internal layers are etched, but before the external layers are etched).
Unfortunately GoldPhoenix don’t specify this. From my experience with them, you should be OK with 0.007" or 0.008" annular ring for outer layers, but I wouldn’t go less than 0.010" for inner layers.
As always, don’t go smaller than you really need, as the yield and reliability will be better if you have more margin for error.
Personally 0.005" seems to small to me, considering the drill registration - it doesn’t take much for the hole to be right on the edge of the pad. Some cheap suppliers like Olimex are are sometimes off by about this much with their drill reguistration - I wouldn’t uise less than 0.010" annular ring with them.
I thought the same when I converted it to mm - it’s 0.127 mm - which is small for a low-cost supplier. PCB Pool can’t even manage that, their minimum annular ring is 0.15 mm. I often use 0.6 mm vias with 0.3 mm holes.
Looking at goldphoenix, they seem to have the capability to go even lower, 0.2mm hole and 0.1mm traces. Could not find min annular for via. So I would think it has more to do what capability they are using for the BatchPCB service.
I’ve been pretty happy with GoldPhoenix, but I’m not sure I’d be brave enough to try 0.4mm pads with 0.2mm holes.
No mater what supplier you’re using though, there’s no sense in using smaller tracks / annular rings than you actually need. Yield will be lower, cost will be higher, and potentially reliability will be affected too.
I’m going to start doing the layout with a larger via, and if things get tight I might go smaller. This is a one off project for myself so it is not that critical.