AFAIK the size of the mempool impacts the mining date, not the broadcast one.
Each node has a maximum size in megabytes which it will use to store unconfirmed transactions. If it hits that limit, then any transaction with a fee lower than the lowest fee transaction it is currently storing will not be added to its mempool and will not be broadcast to other nodes.
Which other block explorers are showing broadcast dates please? I only know one other.
https://live.blockcypher.com - mouse over the "Received" box to get an exact time
https://explorer.bitcoin.com - under "First Seen"
I don't find this data on those ones (only the mining date)
Yeah, the time given on blockchair.com is the time the transaction was received only for unconfirmed transactions. Once the transaction is confirmed, the time updates to the timestamp of the block it was confirmed in.