I've seen a EUR 1B+ transfer (a transfer from the central gov't tax office to a major municipality with "their share" of income tax constituting a major part of their budget) being executed in the backend, it was really nothing special execution-wise. After all it's all just numbers in a ledger about who owes whom what - just this number was slightly longer than usual.
It would require an extra pair of eyes compared to a 1M payment (which are very common), but that's not a significant difference in process, just one more employee would have it in their queue for approval and it wouldn't even increase the time as it'd jump to the front of the queue of payments that need some oversight. It could involve some extra notification as $1B leaving or arriving is meaningful enough to impact your liquidity and reserve requirements and thus your trading desk might need to borrow/lend some cash.
I'd assume that a major bank might have $1B+ payments quite often - I mean, the T-bond market alone is $500B daily and probably some of the individual trades are larger than $1B; then every delivery of a $1B+ industrial project is probably accompanied by a similar bulk payment and the projects across all the industries add up.
