Extremely long term thoughts on Bitcoin

Bitcoin has a hard cap of 21million, however, is eternally deflationary as people will lose their keys, whether through death, mishandling, improper LN backup, etc

Let's imagine a world 1000 years from now, where Bitcoin has long become entrenched as the first layer of money. What used to be an estimated 5million lost coins has grown to 20million lost coins. With only 1 million in circulation, a single Satoshi has grown to become immensely valuable. Imagine a single Satoshi is worth 1k USD in today's dollars.

Now normally this wouldn't be an issue, because we can gradually reprice everything even further subdividing a single sat on the lightning network. However, if the on chain protocol is entirely immutable and ossified, how will Bitcoin work if we still have to pay at least 1sat/vbyte to send a transaction? (Which can equate to hundreds of even thousands of sats per tx, depending on the fee rate.)

And this problem will continue to exacerbate over time. Will the Bitcoin protocol eventually require a hardfork to address this? And what solutions do you see as possible? Further subdivision of a sat on chain? A tail emission to make up for lost coins that haven't moved in over 100 years?