The Baltics would be joined to the Reich and Germanized.
For a Greater Finland the destruction of Estonian national culture would be a problem, though. Now in control of the lands of Eastern Karelia, Helsinki would have taken on a sort of pan-Finnic manifest destiny and Finland would consider itself the protector of the "brethren peoples" such as Karelians and Ingrians. Before and during WWII there was a lot of goodwill towards Estonia in Finland. The Estonians were fondly considered a sort of a national little brother. Relations were very warm and there were joint military plans and so on. During the war Estonians would have served in the Finnish army, like IOTL, and Finland would have a pro-Estonian lobby that would consider the nation having a debt of gratitude towards the Estonian people.
In these conditions, I could see Finland suggest that the Germans handle the Estonians more leniently than their other Baltic subject peoples and safeguard Estonian language and culture. And it would be easy to see such suggestions bluntly rebuffed. The bloody Finns considering themselves equals to the great German people? The nerve!
If this happens, Finland might try to cut a devil's deal and propose the Germans a wholesale relocation of the Estonian people to a sort of an national reservation in Eastern Karelia. At the time, Finland would be actively expelling Russians from the areas it had annexed. While this would create a purely Finnic Karelia, it would also mean that it would be very sparsely populated. Creating new "Finnic homelands" in the area would help repopulate it.
I don't know what the Germans would say to a suggestion like this. On one hand, they might think that the Finns would be helping them to get rid of the population of Estonia and the area could be more easily settled by actual Germans. On the other, the Germans might see a need for the Estonians as workers to build the Reich and be reluctant to send them to Finland.
Even if such a suggestion was made and accepted, it wouldn't be an easy situation to be an Estonian, having to choose between staying home and being assimilated into the Reich's German population or moving to Karelia, keeping one's language and culture but having to become a settler in a distant wilderness...