Recent progress in second-generation (2G) rare-earth-Ba2Cu3O7-x (REBCO) coated conductors (CCs) has paved the way for the development of all-superconducting magnets generating fields well above 23.5 T, i.e., beyond the limits of the present technology based on Nb3Sn. However, the design of REBCO coils still poses several fundamental and engineering challenges. In particular, the tape geometry and the highly anisotropic electromechanical properties require new approaches for coils. In REBCO magnets, the inner windings' layer changes (passing from the nth layer to the (n + 1)th layer) are particularly critical from the electromechanical point of view as in-plane bending of the tapes results in additional strain that adds up to the bending strain and adds to the out-of-plane winding strain and the strain induced by the Lorentz forces. With the goal of building an all-superconducting 24-T magnet consisting of a 3-T REBCO insert coil in a 21-T magnet, we have determined the mechanical and electromechanical application limits of various industrial 2-G high-temperature superconductor tapes. In a first step, we have investigated the influence of longitudinal mechanical strain on the electrical transport properties of industrial REBCO CCs at the insert's operating conditions. In a second step, we have investigated for these CCs the impact of in-plane bending in different layer-change configurations (layer change in one turn and in two turns). These experiments are accompanied by bending strain calculations linking layer-change configurations and in-plane bending with the tapes' longitudinal strain dependence of their critical current. We present the superconductor characterization, the material selection, the design, and the first tests of this size-constrained 3-T REBCO insert coil for a 21-T LTS magnet.