There's already work in progress to improve Documenter.jl (the package that generates Julia docs) to change the TOC style to something less annoyingly detailed and different from Sphinx [2]. Julia's own manual has grown incrementally, written by various people and definitely needs a once-over by someone who is good at clear technical writing; it's hard to find the time when there's so much other work to be done.
[1] https://github.com/JuliaLang/julia/pull/31954
[2] can't find the PR now but part of a GSoC project
The Julia team and community are constantly advancing the frontiers of language design while grounding it in real number crunching applications. I wouldn't be too concerned about trying to have the same documentation and content approach as the Rust community as their goals were to usurp the mindshare of systems programmers (C/C++) with a novel ownership paradigm.
Looking forward to the progress on error messages.
The "time to first plot" issue bothers me far less than the weak documentation and low-friendliness error messages. I'm not sure where this documentation style comes from that the official Julia docs use, where the left side of the page is permanently taken up with a low information density TOC and the detailed discussion in any real content section is either terse or somewhat superficial, but that imbalance is very frustrating. Try for example to find where in the Multi-Dimensional Array section the eachrow() iterator is introduced. There doesn't seem to be an attempt to develop something equivalent to the Klabnik & Nichols Rust book.
There are some awesome packages in the Julia ecosystem, but the "slap something onto GitHub in one night" style of documentation definitely hurts.
Making error messages more approachable will also help driving toward Julia as the technical computing lingua franca for engineering students.