[Garkin]

EVENT_MANAGER:RegisterForEvent("ChatMemory", EVENT_PLAYER_ACTIVATED, function(event)
   EVENT_MANAGER:UnregisterForEvent("ChatMemory", event) 
 
   local sv = {}
 
   --save current settings
   ZO_PreHook(CHAT_SYSTEM, "ValidateChatChannel", function(self)
      local tabIndex = self.primaryContainer.currentBuffer:GetParent().tab.index
      sv[tabIndex] = sv[tabIndex] or {}
      sv[tabIndex].channel = self.currentChannel
      sv[tabIndex].target = self.currentTarget
   end)
 
   --load settings
   ZO_PreHook(CHAT_SYSTEM.primaryContainer, "HandleTabClick", function(self, tab)
      local tabIndex = tab.index
      if sv[tabIndex] then
         CHAT_SYSTEM:SetChannel(sv[tabIndex].channel, sv[tabIndex].target)
      end 
   end)
end)

Code above works just for primary container, but it should be sufficient as it's not possible to have more chat containers without addons (ChatMultiWindow).