Anadyr Airport (DYR) lounge questions have to start somewhere other than the lounge itself: multiple governments currently advise against travel to Russia, citing safety, detention risk, and limited consular support, and that advisory picture matters far more to your trip than whatever amenities exist at a small airport in Chukotka. Before any lounge planning, check your own government's current travel advisory for Russia and weigh it seriously rather than treating it as background noise.
Anadyr itself, the administrative center of Chukotka Autonomous Okrug in Russia's Far East near the Bering Strait, is served by Ugolny Airport, a small regional field reflecting the remoteness of the region it serves rather than any major hub's infrastructure. Getting to the city itself from Ugolny is its own logistical exercise: the airport sits across the Anadyr Estuary from the town, and travelers typically cross by boat in the warmer months, by ice road once the estuary freezes, or by helicopter, since no direct road or bridge connects the two sides year-round.
Given that access reality, lounge amenities at Ugolny Airport are a minor concern next to the practical questions of whether the trip should happen at all and how you would actually get between the airport and the city if it does. A remote regional field serving a small Far East administrative center was never built around a business-lounge model in the first place, and any focus on lounge access risks missing the more important advisory picture entirely.
If, despite the current guidance, a trip to Anadyr is unavoidable for you, the realistic planning priorities are your government's specific advisory language for this region, the seasonal state of the estuary crossing between the airport and town, and confirmed local transport arrangements, not a search for lounge amenities that a field this remote is unlikely to offer in any meaningful form. Treat the advisory as the first and most important filter on this trip, well ahead of anything to do with a pre-flight wait.