Option clicking in the status menu, can we do it?

So I'll confirm you 100% later when I have my mac to actually test.
I encountered the exact same issue as you.
As far as I remember, what I did was route the mouse pointer to the wifi icon with vo shift fn 5, then turn the trackpad off, and trying not to move the cursor from that location, did a real option click and it worked.
Edit: For wifi diagnostics, when you need it, just type diag in spotlight and you should find it.
Edit: I also remember an applevis podcast or blog post describing this same method to access an option in the boot picker or the recovery menu.

The accessibility infrastructure offers applications the ability to add distinct activation actions to the actions rotor, with the default being Press, and common ones being Drag, Cancel, and Show Menu, in addition to providing the ability to add custom rotors. However as is the case with many first-party applications, Apple is very inconsistent when it comes to following its own design guidelines or conventions, so in this particular case none of the accessibility facilities are actually used and thus your only option is to do what TheBlindGuy07 suggested above.

Editing to replace router with rotor in the first use of the term.

Thanks youu.
A bit unrelated to this thread but since you've brought this up, can you please explain what are those show more details/items (I don't remember the exact term) actions we sometimes have in safari adress bar fore example, and what they are supposed to do when they work as expected? As usual, the documentation is very corporate style and means nothing especially as it seems broken everywhere it could be actually useful.

The Actions rotor, which is not actually conveyed as a rotor on macOS but rather as a menu, has the same purpose as the rotor with the same name on iOS, that is, it is intended to be used to specify what kind of action is performed when the element is activated, so elements that can be activated must have at least one option there, which is the Press action, and elements that provide alternative actions like in the aforementioned Option+Click on the Wi-Fi icon in the Menu Extras section of the menu bar, should provide the same functionality through the actions rotor or menu as well. Beyond the Actions rotor, applications can also create custom rotors usually to move the screen-reader cursor or text input caret to specific elements or positions in text respectively, with some examples being the Headings, Links, or Lines custom rotors.

On the older Intel-based models, if you 'control-clicked' on Display in "System Preferences", you would get an extra option or 2 for Display, such as Screen Orientation even on Macs that did not necessarily support this feature. :)
Not sure if this even exists anymore with the new systems and hardware.

I’m going to file a suggestion to fix this. So you should be able to have an Action to click in the Status menu, correct? This should be found under Rotor
Actions.

You'd think Apple would have added this to the Rotor ages ago. It blows my brain-meats how much the developers overlook these things. 😬

I filed this suggestion.
if you try to find out details about your wiFi connection it talks about
option clicking this isn't possible for voiceover users. please fix this in this area and any other area that should have these kind of actions.

Control+Click opens the context menu, which is the same menu that is opened by a right mouse click, by the context menu key on the full-sized Magic Keyboard, or by pressing VO+Shift+Space, and is not the same thing as the Actions menu, which is an accessibility interface that opens by pressing VO+Command+Space, is intended to contain alternative actions that are normally performed with modified mouse clicks, and may also contain an entry for the context menu named Show Menu.