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Something like meta.com/our_own_tech_handles_this

Not sure it's preferable to hire people at fb salaries to maintain a link shortener than just to use a reputable free one?

Every big company has one of these anyway, and usually more involved (internal DNS, VPN, etc). A link shortener is like an interview question.

They already have fb.com.

their own shortener, e.g. fb.me, presumably

Their own?

fb.com seems like a reasonable choice.