When we accelerate, an event horizon forms behind us resulting in Unruh radiation. In this kind of scenario, the existence of the radiation particles themselves is observer dependent.
My question is: If the existence of the particles is observer dependent, then what do the particles, themselves as observers, observe?
Your question is a bit misleading. Unruh radiation is not about light radiation. Is about thermal radiation. You need to have a field, for example a scalar one $\phi$. The field is full of modes. Now if you make a detector accelerate, it sees the field as it was in a thermal bath, so it means that your horizon acts as a thermal bath for $\phi$. Now the particles are the $\phi$ modes and i hope you understand that asking how $\phi$ sees itself is kinda nonsensical. You need to specify what is your lagrangian/universe content, the motion of each consituent in a chosen frame and then ask what happens to who. As it is it's not very meaningful as a question
A photon is not an observer, and can't be because its proper time is always zero and it has no frame of reference in which it is at rest. However, Unruh radiation is black body radiation, so it does include particles with charge and mass. To get an observer from this, you can get low-probability interactions among these particles that form a Boltzmann brain. This is known as the formation of a Boltzmann brain by nucleation, and it's the scenario commonly envisioned when Boltzmann brains are discussed in the context of the distant future of our universe, which is de Sitter.
What an accelerated observer sees as a detection of a quantum of Unruh radiation, an inertial observer sees as the emission of a quantum by the detector. I don't see why this analysis would change if the inertial observer is a Boltzmann brain. The Boltzmann brain can also say, "I think, therefore I am," but according to an inertial observer the brain never existed and never had that thought.
