Did you just go for 3.0, or did you do “baby steps” in between? (e.g. 1.138 > 2.0 > 3.0)

Pretty much that. Downloaded the latest compose.yml, copied all the relevant bits from my existing compose file to the fresh one (volumes, database/db credentials, etc), set the version to v2.0.0, and let 'er rip. Made sure it was playing nice, then checked all the changelogs up to 2.7.x (whatever patch was the newest last week), set the version to v2, and updated it again.

Fast forward to this week, all I did was set the version to ‘v3’ and the update took without a problem.