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Those batteries must be for powering electronics that receives commands from your controller or remote.  They don't have anywhere near the energy to raise something like the headrest of a normal bed.

However, that has nothing to do with why one of them failed.  I've never seen a 9 V battery fail like that.  All I can think of is that one of the cells had a fault that grew over time, eventually shorting the battery and failing in a spectacular way.  Even that surprises me since these seem to be primary cells, so there wasn't extra energy available from a charger.

In short, an old battery failed.  It is hard to say why, and it really doesn't seem that it is due to anything you did.

If those actually are rechargeable, then possibly the charger failed and over-voltaged the batteries.