What is the purpose of this plastic piece inside my MacBook Air?
It is a structural connector and should be repaired and replaced. The battery is part of what makes the case stiff so your device will be more susceptible to bends. Not having the bottom cover latch in could damage the batteries in a very unsafe way. Same if that piece or even a tiny screw were wedged between any part of the top case or bottom cover and the battery thereby pinching or puncturing the exposed cells.
Rather than risk a fire, I would have someone trained on Mac repairs examine your Mac and evaluate of it’s safe due to any chance a piece of plastic or screw was loose inside. The linked article you mentioned has a much less fragile battery and isn’t as susceptible to torsion due to a fundamentally different case structure design. Your battery has less armor than the older ones and safety depends entirely on zero loose parts being inside the case.
A proper fit of the bottom plate for ensured protection and structural integrity. Zero debris ensures safe operational conditions.

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