I think your problem was more that you assumed the senior was acting in bad faith by doing what he was doing in your question. Questions are best recieved when they come from a neutral tone, state facts rather than opinions and thoughts, and have a clear goal. Yours lacks all of these. And your question:
How can we make him code without burning bridges?
Is very very slanted. It reads like a rant. If you want to be taken seriously just spell out what is going on, then say what your concerns are, and what you want to achieve by asking the question. If that goal you want to achieve is reasonable you should get good answers. If you insert your opinions into the facts of what is going on it looks bad.
The problem is that instead of coding, as our manager told him to
before going in holidays, he keeps just telling us to code things
saying "he's too busy to code", most of which are easy things to code
that would be perfect for him to familiarize with the code.
There is nothing in this paragraph that is factual except that he says "he's too busy to code" all of the rest is full of your opinion of what the manager told him and what you think he should be doing. None of this makes for a good question. Your whole question is full of places where you inserted your opinion into the issue instead of just telling us what is going on and what you would like to see changed. That makes it feel very ranty.