Hi Joshua,
That's interesting. When you mouse over a link, you don't get a tooltip that could point to WebView2 as a possible cause, which would match some other comments on this thread.
Generally speaking, you will see this on most websites. If you hover over a button or anchor(text link) tag, you will get a tooltip displaying the title attribute's contents on those HTML tags. However, of course, in a full browser, you can see the destination at the bottom left in the case of anchor tags as they have a href attribute. As such, you should at least get the standard functionality of a tooltip containing the title attribute of a link because the new Outlook app is just a progressive web app(PWA), and it's rendered in WebView2, and that is just a mini Edge browser.
Regarding Edge, I wonder if the users having the issue with the tooltip don't run Microsoft Edge but instead opt for Chrome or some other browser. I suggest this because the WebView2 runtime is part of Microsoft Edge. As such, when Edge updates, so does the WebView2 runtime.
Microsoft is aware that people may not always use Microsoft Edge; as such, they offer a distribution of the WebView2 component that any developer can package with their PWA-based applications. Microsoft almost certainly distributed a version of WebView2 with the new Outlook app to ensure it worked. However, if Edge isn't updating the WebView2 component, then you have to wait for Microsoft to update the component and distribute the update via an update to the Outlook app. This is likely slower than if you had gotten the update through Edge.
For reference, I'm presently running Edge/WebView2 Version 128.0.2739.79.
You can download the latest version of the WebView2 component and install it yourself should you need to by going to the following URL.
https://developer.microsoft.com/en-us/microsoft-edge/webview
If updating WebView solves the issue in your test environment, you could push out the MSI installer via SCCM to ensure all devices on your network are on the latest version.
The worst part is that Microsoft went out of its way to disable the status bar in WebView2. You can see in the documentation by default that this is enabled, and this is the same function you would see in any browser, which shows the URL destination at the bottom left. Enabling this would likely fix this problem for everyone.
https://learn.microsoft.com/en-gb/dotnet/api/microsoft.web.webview2.core.corewebview2settings.isstatusbarenabled
I don't believe this is an attempt by Microsoft to push people to use Microsoft Defender, though I can see how someone could come to that opinion, given the situation.
My theory on how we go here is that Microsoft wants to save money on developing its various email applications. The first step in that process was picking a single application to use going forward, and that application was the one that runs on outlook.live.com. It's already a PWA. It'll run on any OS with a browser supporting PWAs. This allows Microsoft to divest itself of the old Mail clients and the various Outlook desktop apps. It can likely also replace the Exchange OWA web app with the new application. Instead of developing/managing a half-dozen or more applications, Microsoft can now focus on one.
I did run a quick test, and the issue with not seeing the URL when mousing over a link also exists on outlook.live.com when you disable Safe Links. You would only see the URL if it's in the Title attribute. As mentioned above, you can see the URL in the status bar at the bottom left of the browser window, so it's less of an issue.
Of course, that's the final workaround, and it's highly impractical. You tell users not to use the new Outlook app to view emails, though you may want to keep it so you get nice notifications of new emails and ask them to use the following link instead for viewing and reading emails.
https://outlook.office.com/mail
You will at least see the URL of links in the bottom left corner of the browser window.
However, if you can switch back to the classic Outlook and use it for as long as possible before you are forced to switch, hopefully, Microsoft will have fixed it before you are forced to use the new Outlook.