Both exist and the choice tracks whether the 365 account survives your departure:

The one time copy, right when the account is dying: export from Outlook on the web, People, Manage contacts, Export contacts, producing a CSV of everything. In Thunderbird open the Address Book and import through its Tools or the import wizard, choosing CSV and walking the field mapping screen where First Name, Last Name and the email columns pair up against Thunderbird's fields, the two minute chore that decides whether phone numbers land in the right slots. Done before the account closes, the loose end ties off permanently.

The live sync, worth having when the account persists, a personal 365 subscription or an ongoing relationship with the org: the TbSync add-on with its Exchange ActiveSync provider connects Thunderbird to the 365 contacts as a synchronized address book, edits flowing both directions on its schedule. Setup is the two add-ons installed, a new TbSync account of the EAS type signed into the mailbox and the contacts folder ticked for sync. It rides add-on maintenance cycles as such things do, but it turns the loose end into a living connection rather than a snapshot.

For the leaving a job shape specifically, the one time CSV is almost always the answer, taken in the final week alongside the calendar's ICS export from the same OWA neighborhood, the pair covered from the export side in the departing employee thread linked alongside.