Here is a plugin-less solution that I personally use and think works very well:
cnoremap <expr> <Tab> getcmdtype() =~ '[\/?]' ? "<C-f>i<C-n>" : "<C-z>"
It makes <Tab> trigger Ctrl-f, enter insert mode, and start vim builtin completion if in search mode. Otherwise, it ...
Make a mapping, say,
nnoremap <leader>v :Vimspector
Note that it doesn’t end with a space or return or anything, so when you type the mapped characters you’ll be waiting at a partially filled prompt.
You could even add <C-z> (assuming that’s what your wildcharm is) to trigger completion.
It is likely that there are other commands that start with :Vim but not :Vimspector that are being offered in the completion, hence why it stops there.
Natively, vim offers the :VimballList command. You can see with :h :VimballList that this comes from the pi_vimball standard plugin. That page will tell you that if you do not wish to use this plugin you ...