Currently, you can only chop them up into atoms worth 1e-8 BTC (satoshis), but there isn't much that needs be changed in the code and the protocol to get that to much finer grained.
Therefore, it's unlikely that there will ever be zero bitcoins.
Such a change would be a hard fork and, as you know, we don't do that in Bitcoin. But, no worries because we have millisatoshis in Lightning. Because Bitcoin scales in layers, each layer can implement more and more divisibility as required.
https://bitcoin.stackexchange.com/a/69704
As you said, bitcoin is infinitely divisible, therefore the world economy can run on 1 btc or 1 satoshi.
True, it'd be a hard fork. However, I don't believe hard forks are impossible if managed properly.
The taproot upgrade (not a hard fork, I know) was rather uncontroversial and accepted rather easily.
I suspect a hard fork allowing for - say - bitcoin amounts encoded in 64 bits would not necessarily generate the kind of upheaval the blocksize wars did.
And, hopefully, even for controversial upgrades, the lessons of said wars will have been learnt and the process of upgrading Bitcoin can be done in a slightly more reasonable / orderly fashion.
In a world where only 1,000,000 BTC remain in circulation if one person owns 500,000 of them means he controls half of the total value of BTC and that everyone else's coins will add up to the other 500,000 BTC, and being able to divide the each BTC into smaller and smaller amounts doesn't change that fact. Whether we can divide 500,000 BTC into 50 trillion Satoshis or 5 quadrillion "New Satoshis" worth 1e-10 BTC each doesn't make new wealth appear.
Therefore, over a long enough time scale, the number of available BTC tends towards zero.