Do you have recommendations for the minimal text size in logos in general? The example shows a text logo including its claim. What minimal font size would you recommend with or without claim?
Since you're asking this in the UX stackexchange I'm assuming you're talking about the size on a website or app, instead of a brochure or business card for example.
I've generally found that 12px is the smallest you can go, sometimes even 10px, but that really depends on the font you're using.
I've found most others also recommend 12px as a minimum, e.g.:
Penn State: https://accessibility.psu.edu/fontsizehtml/
The English government starts at 14px for the smallest text: https://design-system.service.gov.uk/styles/typography/
In your case I would probably also go for at least 14px since the "People. Positions. Careers." is using a thin font which will be harder to read by default in smaller sizes.
If the logo would take up too much space with the claim at 14px in size, it might be better to remove the claim (e.g. hide it on mobile devices but show it on desktop).
For the "Conusio" part, I would probably go minimum of 12px but since it's a logo you would probably want that a bit bigger. Also that part might not be text but maybe a vector element which would mean you'd have to set a width and height instead of a font-size.
Also, normally a graphic designer who makes a logo would provide the minimum dimensions the logo should have.
Best thing you could do is to do some A\B-tests. Decide on a font-size, check it on different devices and show it to some other people to see if they can read it since there's no one-fits-all solution.
This question needs context to get an ideal answer: building sign, business card, favicon?
Anyway, as described in this answer, a logo is no longer a static object, becoming an element adaptable to the medium where it will be used. Instead of measurements or sizes, it is preferable to establish proportions (minimum or maximum) depending on the context in addition to graphic variables for other applications.