Distinction I have not seen addressed: I do not want my Thunderbird contacts merely in desktop Outlook's local folder, I want them in my Outlook.com account itself, so my phone and the web see them too.
Does the import land server side or do I need a different route?
Good distinction, and it hinges entirely on where the import lands. Contacts imported into a folder belonging to the Outlook.com account sync everywhere, contacts imported into a local PST stay marooned on that one machine. Two routes guarantee the server side landing:
Browser route, no desktop Outlook involved: export the Thunderbird book as CSV via Tools, Export in the Address Book window, then sign in at outlook.com, open People from the app launcher and use Manage, Import contacts with that CSV. The import happens directly on the server, so phone and web pick the contacts up on their next sync. This is the route I would take, nothing can land in the wrong place.
Desktop route if you prefer the richer import wizard: in desktop Outlook run the CSV import as usual, but at the destination folder step deliberately select the Contacts folder shown under the Outlook.com account, not the one under any local PST. Same wizard, different branch of the folder tree. That single click decides marooned versus synced.
Verify the landing either way by opening the People app on your phone a few minutes later, appearance there proves the contacts live server side.
Browser route, and the contacts hit my phone within minutes. That folder tree distinction explains why my last attempt years ago never synced.