For the most part the menu bar has no configuration options in respect to font, size, etc.
You can however manage the icons in the menu bar by holding command while clicking & dragging them. This allows you to re-arrange the icons or drag them off the menubar to hide them.
As others have suggested, I'd encourage you to submit feedback to Apple regarding any customization changes you'd like to see in future versions of the OS.
Apple Mac OS X Feedback
There is actually an easy fix for this, as it turns out.
Abilitynet.org has a nice clear description at https://mcmw.abilitynet.org.uk/apple-os-x-10-10-yosemite-making-text-larger/
I didn't discover that source until after I'd called Apple Support, where I was given the same very simple answer, which is:
On the Apple Menu, go to System Preferences. In System Preferences, go to Displays. Change from Default to Scaled, then click the box to the left of the Default box to choose larger font or gigantic font. (Unfortunately, the Scaled display options are not available with a slider, which would have been perfect as then you could choose exactly the size that works best for you. However, the next size up from Default will probably work well for almost anyone who's been struggling to read the menu bar.)
Making this change not only fixes the visibility of the menu bar, but also carries over to other application menus. For example, I use WORD, and was having to peer at my 27-inch screen from 2 inches away to see where to navigate the cursor in order to change the font size for my document. In Google, if I wanted to read an url, I had to copy and paste it into WORD, then zoom the text display. It was VERY frustrating, and now all of that's just a bad dream.
((As an aside, as a "newbie" to the Apple world, this was my first contact with Apple Support and they earned top marks from me for response time, courtesy, and giving me precisely the info I needed. Thank you Apple Support!)
Best Answer
I'd guess at 11pt, SanFransisco.
Standard list views are 12pt, the headers are smaller, but not small enough to be 10.
You can test by eye...
Open any finder window
Hit Cmd ⌘ J
Change the text size until it appears to match the status bar.
Zooming the screen might help comparison [ Opt ⌥ + scroll wheel by default]
This is a quick attempt at matching, artificially zoomed in Photoshop...