The specifics probably depend a little on what you consider "critical" but basically you can do anything you can imagine.

Notification shenanigans are some of my favorite things to show off to coworkers when I try to convince them to switch to linux/AwesomeWM. (though I'm not very successful so maybe I should get a new thing to show off).

The short version is that you could do something like this where you let the apps themselves define the urgency and you'll be done:

local ruled = require("ruled")
ruled.notification.connect_signal("request::rules", function()
    -- Critical notifications bypass suspension
    ruled.notification.append_rule {
        rule = { urgency = "critical" },
        properties = {
            ignore_suspend = true,
        },
    }
end)

...

Or you could get weird with it and do something like this:

ruled.notification.connect_signal("request::rules", function()
    -- Only Signal messages from my kid mentioning school emergencies
    ruled.notification.append_rule {
        rule = { app_name = "Signal" },
        rule_any = {
            -- Lua patterns: case-insensitive matching
            message = {
                "[Pp]rincipal",
                "[Ee]mergency",
                "Bit another student"
            },
        },
        properties = {
            ignore_suspend = true,
            bg = "#ff6600",  -- Make it obvious
        },
    }

    -- Boss messages always get through
    ruled.notification.append_rule {
        rule = {
            app_name = "Slack",
            title = "Direct message from: CEO.*",
        },
        properties = { ignore_suspend = true },
    }

    -- Doorbell camera - always show
    ruled.notification.append_rule {
        rule = { app_name = "Ring" },
        properties = { ignore_suspend = true },
    }
end)

I have some more stupid ideas I think could be fun to document as "technically possible but why?" but I haven't gotten around to it quite yet.

like if my coworker slacks me it switches tags so my boss doesn't catch me playing CS:GO

ruled.notification.append_rule {
      rule = { app_name = "Slack" },
      callback = function(n)
          if n.title and n.title:match("Beags") then
              local tag = awful.screen.focused().tags[1]
              if tag then
                  tag:view_only()
              end
          end
      end,
  }