iirc, build accepts variables in the 3rd argument .build(queryClient, options, { variables })

Since it was really bothering me, I went looking into the code and found the answer as to why it does not work.
When displaying the content of the mutation retrieved from the cache, the state contains the expected variables.
But, in the execute function from the mutation class file there this line of code (l. 202):
this.dispatch({ type: 'loading', variables: this.options.variables! })
As you can see, it takes variables from the mutation options and that's where things go wrong.
Because the dispatch will set the mutation state variables with options variables passed as action.variables parameter:

case 'loading':
          return {
            ...state,
            context: action.context,
            data: undefined,
            failureCount: 0,
            failureReason: null,
            error: null,
            isPaused: !canFetch(this.options.networkMode),
            status: 'loading',
            variables: action.variables, // <--- here
          }

But after the mutation is fired, the "variables" field of options does not exists anymore.
And when onMutate is called with mutation state variables after the loading dispatch, it's actually undefined now...
So it's impossible to fire it again just by calling execute. First we need to set the options.variables using the state.variables.

export const updateProcess = async () => {
  const mutation = queryClient.getMutationCache().find({ mutationKey });
  if (mutation ) {
    mutation.setOptions({...mutation.options, variables: {...mutation.state.variables}})
    await mutation.execute();
  }
};

Now I'm able to work around the issue, but my question is why the options.variables is removed. Is it meant to be like this for a reason ?

this is still the best way:

#6743 (comment)

they are part of the public, low-level query-core API. Most of it isn’t documented but it’s also not going away. Feel free to update the docs if you want.

Thanks for the confirmation! And I agree, in an ideal world, most users wouldn't need to use the low-level APIs. My world is definitely less than ideal 😄