Does this mean that my car doesn’t belong to me when it’s in the shop?
See "mechanics lien."
And when you put money in the bank, it is, as a matter of law, the bank's money. You retain a claim on some of the bank's money, but the money is not yours.
You do not own 'your' motor-vehicle, whether it is in the shop or in the garage of the building you are a resident of.
There is an allodial title to the automobile you purchased, and it is held by the motor-vehicle registry. You merely have a 'Certificate of Title'. They have an MSO/MCO, or Manufacturers Statement/Certificate of Origin - the allodial title.
[for similar reasons, you don't own the building you reside at]
Actually the mechanic does own it until you pay him for repairs. It’s called a mechanics lien.