This is a lot of posts. Will I have to manually edit all ~150 of them because my accounts merged, to ensure that I earn publicity badges? I don't wish to spend many months doing a few posts a day to work around the lack of server-side automation, nor do I want to spam the front page with hundreds of bumps for posts which I have made no constructive edits to.
Yes, all of the links would need to be changed to continue counting towards your progress. While all past progress should have been rewritten to the single Id at the time of the merge, there is no concept of "forwarding" one Id to another for user profiles.
On the backend, the profile that was merged is a deleted user. It effectively changes the owner Id attached to everything on that profile (posts, comments, votes, etc) and then deletes the profile like any other user deletion once it's empty. Anything further pointing to that Id is ignored, including a profile link to the old Id which would now 404.