Speaking from my own meditation & physical opinions only:

Relaxed and limp are two very different words. Ideally when you're meditating (or really performing any task) you will want to be as relaxed as possible. This means you're using the minimum amount of strength to hold your posture, a posture which should be as upright as possible which can require getting used to if it's new to you.

To get a better idea you can hold your arm out to your side and flex it while holding it still, reverse this process as far as you can while still keeping it elevated to understand the sensation you're aiming for. Everything should be light, loose. Most people walking around will carry their stress in particular areas of the body, which you can observe in where they hold more tense and flexed. Your objective is to remove any tension you're holding and relax every muscle.

In my opinion you should absolutely not lean against the chair or anything, not slumping or being supported by anything you can avoid needing. I believe meditating isn't an attempt at "going to sleep" as you would by curling up or laying down, but instead your goal is to reach a point of comfortable consciousness where you can voluntarily access subtle portions of your psyche you would normally be too distracted to perceive.