(this was mostly the pre-iCloud-Drive backup solution that was itself a holdover from iTools) I think technically anything that points you to a place where money could be made is an advertisement, and even advertising mDNS devices on a local network is doing the 'hey you, there is a thing over here'-thing. But there is a big difference between creating a universal spot in software to load arbitrary advertisements for new products vs.
in-product purchase options (which obviously tend to lean more into the upsell category of ads than the nudge for mindshare category of ads). The whole 'try safari' thing is one I do actually see on new accounts, and sometimes on first startup with browsers, but IIRC once dismissed they don't come back again. Heck, it even is less persistent than the post-install highlights notification you got from major OS upgrades. Perhaps the Browser-notification is best compared with Microsoft's OneDrive notification in the Security settings where they suggest that using a free OneDrive account is the 'One True Way' to stop ransomware.