At first, "Searching" sounds like a love poem about someone who has left. The speaker says they are still searching and always will, and we expect the next line to name a lost person. Instead, the poem turns: they are not looking for "you" at all. They are looking for "the piece of myself / I gave to you."
That twist changes the whole feeling. The speaker isn't begging for someone to come back. What hurts is the loss of a part of themselves, perhaps trust, openness, or innocence, handed over in a relationship and never returned. The poem doesn't say what that piece is, which lets readers fill it in from their own experience.
The mood is quiet, tired, and a little resigned. "Always will" sounds calm, almost final, as if the speaker has accepted that the ache won't fully go away. The short lines and plain words make it feel honest and unguarded, like a private thought said out loud.