It is a GOOD thing that climbing doesn't work in the tutorial
Think about it. What is the purpose of a tutorial? To teach you how the game works and what you can expect. Manage expectations. And stuff not working properly is undeniably an absolute core mechanic of Helldivers 2.
Can you imagine the confusion of new players completing the tutorial without encountering a single bug or dumb design decision, expecting the rest of the game to be exactly like that and then playing their first mission? It would be madness.
Those poor newbies would be so confused why the tutorial is so different from the rest of the game. This just shows the real genius behind Arrowheads dev team.