The Dirac equation can be derived basically "directly" from the Representation theory of the Lorentz group for the spin half representation, this is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) 6.3 "Dirac Equation".
As mentioned at spin comes naturally when adding relativity to quantum mechanics, this same method allows us to analogously derive the equations for other spin numbers.
- Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=743
- www.youtube.com/watch?v=zM-Lc16nyho&list=PL54DF0652B30D99A4&index=66 "L3. The Dirac Equation" by doctorphys
- Video 5. "Dirac equation for the electron and hydrogen Hamiltonian by Barton Zwiebach (2019)"