Could observer effect cause electrons in one orbital to be found in another? The observer effect states [1] that

when unobserved, absolutely small particles like electrons can simultaneously be in two different states at the same time.

If we look at an atom of any element, all of its electrons are subject to the observer effect. As the electrons are known for wave-particle duality, the Schrödinger equation can be solved to yield a wave function for each electron in the atom. An orbital is a probability distribution map of a wave function squared, and each orbital can accommodate up to two electrons.
For a single electron, it is not hard to imagine that the observer effect operates upon it to the extent of the probability distribution map specified by its orbital. That is, the electron can simultaneously have two positions if unobserved, and these two positions will not go beyond the space occupied by its orbital.
However, I'm wondering if an electron can have two positions when unobserved, where these positions are in different orbitals. For example, an electron falls under both the $\mathrm{2s}$ orbital and the $\mathrm{2p}_x$ orbital, if unobserved, and observation forces it to collapse into either $\mathrm{2s}$ or $\mathrm{2p}_x.$
Reference

Tro, N. J. (2015). Principles of Chemistry: A Molecular Approach, Global Edition. United Kingdom: Pearson Education Limited.
Your intuition is exactly right. Let's consider an atom of neon. It has ten electrons, which we describe as being in 1s, 2s and 2p orbitals. But the electrons are indistinguishable from each other, and accurate wave functions allow all of them to be in all orbitals. Only when we make a measurement (or some other sort of &quot;observation&quot;) do the electrons behave as if they are localized to individual orbitals.
For example, if we measure the binding energy of the electrons by photoelectron spectroscopy, the result will always be an eigenvalue of the energy operator (aka Hamiltonian). But that does not mean that any one electron had exactly that energy prior to the measurement. As is always the case in quantum mechanics, systems that have multiple eigenstates exist as a superposition of those states until the measurement, the result of which is always one of the possible eigenvalues rather than, for example, a weighted average of them. So we will measure binding energies consistent with 2p orbitals, 2s orbitals and 1s orbitals with an intensity ratio of 3:1:1.