[Ketho]

I would have expected GetSpellInfo() to return the school of a spell but I was wrong

You can still get it from listening to CLEU
(this example does not take channeling spells into account)

local playerGUID = UnitGUID("player")
 
local f = CreateFrame("Frame")
f:RegisterEvent("COMBAT_LOG_EVENT_UNFILTERED")
f:SetScript("OnEvent", function(self, event)
    self:OnEvent(event, CombatLogGetCurrentEventInfo())
end)
 
function f:OnEvent(event, ...)
    local timestamp, subevent, _, sourceGUID, sourceName, sourceFlags, sourceRaidFlags, destGUID, destName, destFlags, destRaidFlags = ...
 
    if subevent == "SPELL_CAST_START" and sourceGUID == playerGUID then
        local spellId, spellName, spellSchool = select(12, ...)
        print(format("Casting %s (%s)", GetSpellLink(spellId), GetSchoolString(spellSchool)))
    end
end