Learning is a core part to general intelligence, as general intelligence implies you can learn about new problems so you can solve those. Take away that and you are no longer a general problem solver.
A rule based expert intelligence system can be highly intelligent, but it is not general, and maybe no arrangement of rules could make one that is general. A general intelligence system must be able to learn and adapt to foreign problems, parameters, and goals dynamically.
The classical example of a general intelligent task is to get the rules for a new game and then play it adequately, there are AI contests for that. That is easy for humans to do, games are enjoyed even by dumb people, but we have yet to make an AI that can play arbitrary games as well as even dumb humans.
Note that LLMs are more general than previous AI's thanks to in context learning, so we are making progress, but still far from as general as humans are.