As an EMT-B patroller (retired now) the medical stuff I carried was mostly ABC things - CPR mask (compatible with the O2 system), OPAs and NPAs (don’t know if those are in OEC protocols), tongue depressors, gauze pad assortment, abdominal pads, kerlix, triangle bandages, bandaids (Snoopy, Spider-Man, Wonder Woman), glutose, aspirin (for cardiac, again I’m unsure about OEC), vinyl gloves, etc. On cold days I’d sometimes carry chemical heating pads, but they either leaked or activated if I carried them too long. I think I posted a list here upthread.
But as to how to pack a vest, I grouped airway stuff in one pocket, bleeding stuff in two others, meds and such in one pocket, paperwork and manual in one, tools (vise grip/leatherman, zip ties, etc.) in one, rescue stuff (rope, webbing, ‘biners, brake, slings) in the back pocket. That way I could reach for what I needed from memory without having to paw through different things. In my system, bleeding stuff, tools, and PPE was in the left side pockets, meds and airway on the right side. If you develop a system based on your personal logic and associations then you can reach stuff quickly (and hopefully not look like an unprofessional goof).
Incidentally, I didn't carry splints or (much) other stuff that wasn’t ABC. We had trauma, airway, medication, and rescue response packs at the top stations full of all the possible stuff that could be delivered quickly enough - my focus was on assessment and stabilization, then radio for the cavalry. For some reports, if we dispatched from the top stations we’d carry the appropriate response pack.