How to 'close gate' after player death?

You disabled the entire input system so it can no longer detect keys going up. You should be able to tell the controller to flush input manually:

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Another way is to not disable input but instead work with the Enhanced Input system. That’s what Mapping Context is for - you can add, and you can remove it on the fly. The whole thing or parts of it, and override priority.

It can also flush.