How to get the line numbers for all matches?

Doing two manual passes over the text is rarely needed. Most often one just does

g/^test/DoSomething

And that's enough. The reason is that :g is implemented in two passes, so it's not a problem if you, say, add a few lines after each match.

However, if you really want those numbers in a List, you can achieve this with the same pattern:

let temp = []
g/^test/call add(temp, line('.'))

A convoluted (and untested) way I sometimes use. The idea is to use map() to associate line numbers to the actual (matching) lines, then filter() to keep only the matching lines, then map() again to return only the line numbers

" Note: This code uses lambdas and vim 8.{recent} methods.
:echo getline(1, '$')->map({l, v -> [l+1, v =~ 'test']})->filter({k,v -> v[1]})->map({k,v -> v[0]})

Another convoluted approach consists in using a function that permits to apply changes as matches are found (still untested)

:let g:lines = []
:call getline(1, '$')->map({k,v -> v =~ 'test' ? add(g:lines, k+1) : g:lines})
:echo g:lines

" or 
:call map(getline(1, '$'), {k,v -> v =~ 'test' ? add(g:lines, k+1) : g:lines})

Note: we could also use :global which is much simpler (see Matt's answer) but as it messes search register and cursor position, I usually avoid it when writing plugins.