> I'm planning on going in January
I have been there years ago. Nordavia did flight from Talagi Arkhangelsk main airport. Weather being unpredictable it's impossible to tell if a flight will have much delay or be canceled, so it's good for travels with flexible time.
Solovki airport is undergoing renovation. A first stage has just been completed but the whole is expected to be operational for the next summer tourist season. This is a federal project done in coordination with UNESCO.
When the runway was out of service, a Mi-8 helicopter was doing the route from the airfield at the south of Arkhangelsk, Vaskovo, tickets bought locally only.
Runway only has just resumed service and small L-410 propellers are supposed to be in service from 02.12 with same frequency than before (3x/week), as per local online gazette:
https://www.pomorie.ru/2019/11/29/5de0f914764de95b5378b1b2.html
Vaskovo airport does list the route now, at 7500rb, but online booking isn't active, so you better contact them to ask:
http://2aoao.ru/
I will be in Russia between the 26.12 and 03.01, have NYE planned in SPb, but wanted to relax in the meantime in the north, and was thinking of Solovki, but 15.000rb (both ways) for just two or three days and with the uncertainty in schedules because possible bad weather, I just forgot about it and will relax instead in northern Vologda province. But then about Solovki, that's the most recent info, yet because I decided not to go anyway, i didn't bother to contact Vaskovo about the new route,