Is it? It's a nudge at best, which you can probably taxonomize as "advertising" but its for a thing you already have and users genuinely might not have noticed.
Now, they had a different notification in the past for MobileMe that was truly an ad because you didn't have to be an existing customer for an upsell nor did it come with the OS by default (this was after iTools got rebranded by Apple), and it just wanted you to go to their website to look at the product and maybe buy it, download it and install it. (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.
I think the fact that you already have the app installed is not a mitigating factor, it actually makes it worse: I can't uninstall Safari. They put it on my computer, I chose not to use it, and now they're specifically targeting other applications they want me to switch away from.
It's not only a new installation issue either; I've had this laptop for 7-8 months. It's only happened 4-5 times, and I assumed (without verifying) that I get it whenever Safari has updated. For what it's worth, I have turned off notifications from Safari; this is the OS itself saying "I see you're using another browser; have you thought about using ours instead?"
I guess it's perspective-dependant. Computers are really more sold like appliances the last decade or so, and as such the specs they are sold on depend on the combination of hardware and software. For the general consumer, any deviation from the expected and advertised performance would be A Bad Thing™, and modifying the base facilities would count as such.
Now, for me (and perhaps you too) I see it much more as a collection of interconnected hardware devices, with various firmwares in ROMS and Flash EEPROMs, boot loaders and operating systems on mass storage devices, and a few ISAs, ABIs and APIs to make sure it all works to a certain standard. In practical terms, that doesn't really matter to anyone else, not to Apple, but also not to Microsoft, HP, Dell etc. So we're back at "the thing is a black box appliance" and as such, the base advertised features should be properties of the appliance as bought by the customer. This also means that any deviation from that will either mean someone has to spend (or waste) time and energy on telling an angry customer that their BitCoinBrowserXXL is the reason the battery is empty after an hour, and that it is their own fault, or that the device is defective, or that the advertisement was false. If you are a for-profit company, would you not cut that "waste" of support by 33%?
There is always the fear that the company is doing an evil thing and wants to harvest your life, but if Apple wanted to do that, they could. It's more likely that it's just part of the energy saving subsystem to direct users to optimal usage scenarios and things like "dim display automatically" and "use safari" are part of those scenarios. There really isn't much else gained by using Safari, not by Apple and not by the user. So either both gain a "yes the battery does last longer and the computer is responsive", or they both lose that. There is no PII telemetry in Safari, and cross-device data sharing (like Bookmarks) are encrypted within the iCloud Circle if you are using that, so Apple can't see that either (except if you also enable iCloud Backup on an iOS device), so for data harvesting, it's not really an incentive.
What would be an interesting option is a "do not use notifications to suggest optimal software-hardware interactions" checkbox somewhere so they can just list side-effects near the actual preferences instead of all over the place.
Now, they had a different notification in the past for MobileMe that was truly an ad because you didn't have to be an existing customer for an upsell nor did it come with the OS by default (this was after iTools got rebranded by Apple), and it just wanted you to go to their website to look at the product and maybe buy it, download it and install it. (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.