GoG Galaxy is now how GoG Achievements are managed, no longer through the in-game option (which has been removed). All previously earned achievements, before the switch, have been wiped.
Achievements do not result in a toast or notification so you have to check the client to see what has been earned/has yet to be earned. Click on the Stellaris game in GoG Galaxy, under the My Progress tab to view. You do not need the GoG client open or running for achievements to occur, the client will update the next time you open it even if Stellaris is not running.
Achievements are not enabled by default.
To enable achievements for GoG purchased games you have to change the settings in the Galaxy client. The gear in the upper left corner of the Galaxy client opens a drop down menu and from there you click on Settings, the third option from the top. At the bottom of the Settings menu is Game Features. You will want to check Achievements. Enabling the overlay does not effect if the achievements display a notification or toast, because they don't.
Achievements do not result in a toast or notification so you have to check the client to see what has been earned/has yet to be earned. Click on the Stellaris game in GoG Galaxy, under the My Progress tab to view. You do not need the GoG client open or running for achievements to occur, the client will update the next time you open it even if Stellaris is not running.
Achievements are not enabled by default.

To enable achievements for GoG purchased games you have to change the settings in the Galaxy client. The gear in the upper left corner of the Galaxy client opens a drop down menu and from there you click on Settings, the third option from the top. At the bottom of the Settings menu is Game Features. You will want to check Achievements. Enabling the overlay does not effect if the achievements display a notification or toast, because they don't.

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