That persistent feeling / memory that stays with one after a profound dream?

Solution 1:

Try euneirophrenia

peace of mind after a pleasant dream

(Dictionary.com)

EDIT: Added after the OP's suggestion:

malneirophrenia

In a state of depression following a nightmare:

Glenda's bad dream was so real that she wandered around the next day in a state of malneiophrenia because she was feeling unsettled and emotionally disturbed.

(Wordinfo.com)

Solution 2:

Are you looking for "a reverie"?

"I found myself lost in a reverie of what I had dreamed the night before."

• "the state of being lost in thought especially about pleasant things" MW

examples:

• "I was lost in reverie and didn't realize my flight was boarding until it was almost too late."
• "I felt caught up in a reverie of years long past"