Can the word phalanx also be used to describe the finger bone plus the soft parts around the bone?
It's a great question, and in my humble opinion, the answer is:

Phalanx (plural: phalanges), (also Cambridge and MedicineNet) is the term for one of the bones (only) in the fingers or toes and not for all the "meat" around it. The Google images search for phalanges is quite convincing.

Someone on https://english.stackexchange.com/ might know a word for the whole bone + "meat" part of the finger.