I don’t really think they will move Japkarta.
They will move most of the national government out of Jakarta and create a new “capital city” for the government.
Likely as they do, some major industry and business interests will make similar moves from Jakarta. Civilians will move initially only as their jobs do, or as they chose - if they can. Even then population may not shrink as fast as Jakarta keeps sinking. Nine chances out ten there will be “relocations” of civilians the government will be required to make for stranded civilians. There will still be a Jakarta, even after it sinks a lot.
if it starts sinking maybe they could provide gondola rides for the tourists like Italy does