Jesus’ spirit went to God (Who is spirit), His body went to the grave, and His soul went to Abraham’s bosom/Paradise/Sheol. When He resurrected, His soul, body, and spirit were rejoined, and He ascended to Heaven as our Eternal High Priest to place His Blood before The God on the Heavenly Mercy Seat as the Everlasting Incorruptible Sacrifice. He then came back to earth and walked with His disciples for 40 days, before re-ascending.
I agree with your assessment, although I believe He only ascended after the 40 days here.
Body to the grave, soul to Abraham’s Bosom/Paradise as a compartment of Hades, and His human spirit to God the Father.
After 3 days he was resurrected in the new body, the First fruits, after having also spoken to those incarcerated in Hades, (I believe some reference is also made of His speaking to those bound in Tartarus and even the Abyss).
I recall him giving warning to others not to touch Him until He was presented in Heaven between the Resurrection and the Ascension.