Tech Guru's. Mac Laptop to projector camera. Which inexpensive connector to buy?

amazon.co.uk/Ank…P53

This should work (edited)

Generally there's two types of widget that do what you're after.

There's one that works with USB-C ports that can output a standard video signal (called DisplayPort alt mode) which just convert the DP signal to HDMI. As the computer itself is doing all the video output that should work with any USB or Thunderbolt ports that support this feature (I think it's mandatory for Thunderbolt, but it isn't for USB).

Then there's a second type that's essentially an external graphics card that connects to the computer as a peripheral and generates the video signal itself. These sort do require more support from the operating system of the device they're connecting to and are not generic so some may work and some may not depending on whether software is available. I believe the better ones like DisplayLink do have Mac OS support at the moment.

If the Hama model you have is this one then that appears to use the former:
uk.hama.com/002…mi-

That's a fairly common approach these days, so it shouldn't be hard to find an alternative. It's not going to be cheap cheap since it's a full conversion chip rather than just a plug changer.

I can't find the listing for the second one your purchased so it's hard to say why that may not be working.