I'm not sure what the current state of LibreOffice is when it comes to advanced typesetting, but I expect it could easily do everything in that report.
LaTeX is in a class of it's own, practically the space shuttle compared to a Cessna. Unfortunately, the learning curve is a seemingly endless source of ¡fun! for beginners.
Any templates that are beyond "maths paper in arxiv" level I should look again at?
At the time I thought 'just learn one tool well and use it forever', but now I feel more like 'just use the best tool for the job'. In this case I would say that's InDesign and a few hours of tutorials, mostly. The illustrations you can choose another tool if appropriate.
I would like to have a way to think about when "learn this one tool and use it forever" is appropriate.
Maybe investment in certain kinds of tools pays off more.
Yes. I was quite serious about the space shuttle analogy.
https://tex.stackexchange.com/questions/158668
It can be quite a bit of work configuring custom templates though and any one off deviations are likely to require significant effort as well. There are specific use cases (for example publications with lots of mathematical notation, or the periodic regeneration of tables and charts by a small script) where it can be quite useful.
Most people would probably be better served by a standard office software suite though. Even something as simple as Google Docs is sufficient for the vast majority of documents.
(Seriously though, TeX & Co can do just about anything. https://tex.stackexchange.com/questions/159445 https://tex.stackexchange.com/questions/95783)