Like I wrote, for some integrations it is not possible to gather all the logs. Also how will you know that a client accessing your website in a browser gets 503 instead of your web page?
You don't, but your monitors will show the 503 happening, how often, on which endpoint operation and in which regions; that will give you a pretty good picture of whether is actually your CDN layer or something else triggering the 503
What if it's a specific browser with a specific TLS stack, or something weird?
what if it's green lizard man chewing cables?
one has to start somewhere reasonable and realistic first.