It is not infinitely divisible. There will be 21 million Bitcoin and 2.1×10¹⁵ Satoshi, because every Bitcoin is 100.000.000 Satoshi.

The supply is fixed. Satoshis can't be split up any further.

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Yes they can. It will be a relatively simple change in the code to divide satoshis to 16 decimal places instead of 8.

I remember hearing that some software already uses smaller units than sats.

There's no reason why a person couldn't implement that change already. It doesn't violate the protocol rules in any way.