Does that mean it's also broadcasting them to other nodes for 10 years, so even if miners dropped the transaction, they'll pick it up again?
Not really. If nobody is requesting a given transaction, then mempool.space does not broadcast it by default.
Which is why in testnets, where new miners were joining, mempool.space displayed, that everything is clogged, while miners heard not that much new transactions, and mined half-empty blocks.
And then, people paying 10 sat/vB or 100 sat/vB actually overpayed, while they could get things confirmed at 1 sat/vB without any problems, because miners simply had much less transactions, than mempool displayed.
Since then, I consider mempool.space transaction propagation to be kinda bugged. If you don't broadcast your transaction by yourself, then simply assume, that others may not do that for you, if they have no incentive. Some nodes can store your transaction, and know about it, but not broadcast it randomly, if you won't ask them specifically about this particular txid.
Edit: Also, I am not the first one, who noticed this bug. Similar topic about buggy mempool.space:
https://bitcointalk.org/index.php?topic=5528236