I know officially the games ends at this date and it shows your score with your nation's history.
Can the game be played after this year (and unlock Steam Achievements) ?
There're some mods that allow it, but in the original one, the game ends. You can import your savegame to the Victoria II.
It's important to remark that you can't unlock Steam Achivements in a mod that allow you to play more than 1821, so you need to unlock that achivements before.
You can't unlock steam achievements with mods period, unless they're purely cosmetic which don't affect the checksum. Any mod that changes the check-sum disables achievements.
As for the current game (1.16.3), if you're playing a non-ironman game, you can keep playing as long as you want until 9999.
Iron-man still ends at 1821. Achievements are only available in Ironman Mode, and if the checksum is unaltered.
Also most achievements aren't available to custom nations, except a small handful that generally require custom nations to get anyway.