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That does not work for completions, at least not for me. It works for keymaps, so you can have mode specific (or really any) keymap in src blocks. I have been using his method myself in my init file generator for quite a while now. If you (or anyone) knows/have an idea how to expand it for completions and eldoc, I would be really happy to hear.
At least for Elisp source block one can use font locking to create a custom Capf. Add cape-elisp-block from my Cape package to completion-at-point-functions. Even if you don't want to use Cape you could just copy it to your config. It is a short function.
Unfortunately, the only way I've managed to get code completion working without having to use the C-c ' buffer is through the unofficial copilot.el. The good news is that it work for any language (including elisp literate configs) but it's a little too aggressive on it's completions.