After the connection is made, start a new game. You should start to see Archipelago chat messages to appear, such as a message announcing that you joined the multiworld.
When loading a savegame it will automatically attempt to resume the connection that was active when the savegame was made.
If that connection information is no longer valid, such as if the server's IP and/or port has changed, the Connect Menu will reappear after loading. Use the Connect Menu before or after loading the savegame to connect to the new instance.
If you don't see the Connect Menu within the Main Menu, check that you see a file named `qmodmanager_log-Subnautica.txt` in the Subnautica game directory. If not,
QModManager4 is not correctly installed, otherwise open it and look
for `[Info : BepInEx] Loading [Archipelago`. If it doesn't show this, then
QModManager4 didn't find the Archipelago mod, so check your paths.