Until deployments towards Ukrainian borders began in March/April 2021, the Russians had: the 14th Corps of the Arctic Fleet and the 61st Naval Infantry Brigade very close to the border with Norway in Murmansk Oblast; the 6th CAA in Leningrad Oblast near Finland (okay, technically not NATO back then); the 11th Corps of the Baltic Fleet in Kaliningrad (which in the years leading up to the invasion was massively reinforced with the creation of the 18th MRD) along with the 336th Naval Infantry Brigade; the 76th VDV Division in Pskov Oblast (hence close to the Baltic countries).

During the initial phase of the invasion, BTGs from all these formations were involved in Ukraine, with the exception of the 18th MRD of the 11th Corps and the 80th MRB of the 14th Corps (if I remember correctly), however at that time the BTGs from the 5th CAA had remained in Belarus and had not followed their comrade-in-arms from the other EMD’s units in their adventures around Kyiv. These units were then committed in April/May 2022; the 18th MRD and 80th MRB to reinforce the Kharkiv sector after the Ukrainian counteroffensive in May 2022 and units from the 5th CAA in the Popasna sector (and possibly others).

Today all the maneuver units we know of in the Russian Army are deployed in Ukraine; some elements of the regiments/brigades remain in the “original” barracks, for example, let’s say a battalion of conscripts (from the military service) with perhaps a tank company and other support units. But no full-strength Russian formation/unit is currently in the barracks sitting idle. When Finland joined NATO Shoigu announced the creation of a new army corps in Karelia, and we know of the intention to reform their 11th and 14th Corps into CAAs, but in fact this will be to allocate additional units to Ukraine, and hardly to deploy them to NATO borders, as long as the war is ongoing.

Small edit: I’m not considering the operational brigades of Rosgvardia which may be near the borders and of course the Border Service.