Miner sends small amount of data to pool representing what is required to constitute a low hash from its current stratum template.
Pool submits a submitblock message to bitcoin core with the full block data.
Bitcoin core submits a compact block message describing block header, nonce, transaction IDs, prefilled transactions as needed and extra transactions it thinks may be needed.
The amount of data is variable depending on how much the other node knows, and they may request further data. A full block is only sent to nodes that don't advertise compactblock support.