No large batteries (100MW+), but they are maxing out exporting power to Estonia constantly after that recent nuclear generator came online (which is leading to Estonia having a very clean carbon profile at the moment). Both countries recently signed a MOU to build an additional 1GW underwater HVDC interconnector ("EstLink3"), but it won't be done for a decade.
"Too much clean energy" is a good problem to have! Probably means Finland can pull forward retiring the 2.6GW of coal generation capacity they have (which has been running somewhat consistently at <100MW with the latest nuclear generation addition).
(EDIT: my note: smaller batteries mentioned in other comments for grid support are helpful for phasing out thermal generation traditionally providing grid support services, like maintaining frequency or voltage, but aren't big enough for material energy arbitrage)