Regarding the Apple ITP issue, is it possible that organic traffic is being overstated? There's a hunch in our company that some SEM traffic is falsely being reported as organic traffic and organic traffic is being overstated.
I don't think ITP would affect organic traffic, since ITP mainly affects cookies and organic/paid search is not based on cookies. Could you share more information on that thought process and why you think organic traffic is overstated?
The way our workspace is set up, organic search traffic is calculated as referring domain = one of the known search engines, AND no paid flag. So the concern is that the paid flag is being stripped out because of the ITP issue and not appropriately subtracted.
Typically if you are using a Google or bing SEM strategy then the PAID traffic will report into your search engine data. Unless you are using AMO it will be hard to separate PAID vs Organic. I have seen some people do some processing rules to get closer to differentiating the 2, but that can still be less than 100% accurate. If you create custom ID tagging in your SEM accounts, then search engine referrers will give you the ability to separate the PAID vs Organic.
The paid flag by default is part of the query string, which is part of the URL. As long as that paid query string parameter makes it to your landing page, you should be good.
A common wrecker of query string parameters are redirects. Can you confirm you don't have any on any of your paid search landing pages? Also, can you provide a paid search term where your site appears in results that we can click on and test?