There is really no such thing as a bitcoin, it's just a name for 100,000,000 satoshis. satoshi is the base unit. Lightning network actually further divides this and uses millisatoshi (1/1000 of a satoshi), but ultimately channel settlement is rounded to the nearest satoshi.
If the price rises very significantly, I expect there would be relatively little political difficulty hardforking Bitcoin to increase the precision of the base unit. In such a case microsatoshi might become the new base unit on the blockchain, and the value of pre-fork UTXOs would be adjusted appropriately.
So, it is highly divisible but not infinitely divisible. It can be further divided in Layer 2 solutions but ultimately can't be settled in precision greater than 1 satoshi. However, if it becomes a big problem we will just adjust the base unit.
Increasing precision does not affect scarcity: there will always be less than 21,000,000 BTC, or 2,100,000,000,000,000 satoshi, or 2,100,000,000,000,000,000,000 microsatoshi. It just allows Bitcoin to be transacted in smaller amounts.