Sync is difficult, import is easy. I can’t find Linear’s documentation, but I presume they have some sort of text export; you should be able to import or Watch that without much trouble.
Linear seems to have Docs here, and an API here. Perhaps a Linear user can delve into these for pertinent sections? Trying to understand a doc you yourself don’t use can be confusing - having a start point can help.
Plus don’t overlook AppleScript as part of the glue. I’m not sure if Linear has proper AppleScript support. {Edit: the last isn’t snarky—I just don’t know! Many newer apps see AppleScript as a bit old-school and even apple doesn’t show it much love though it still powers a lot of workflow and inter-app stuff in the macOS universe}.