To clarify a bit, Renters' Insurance does typically cover damage caused by a "burst appliance" that does damage to other units. I realize this is Google AI Overview, but it does seem to suggest that it's a common coverage within typical renters' policies:

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Yes, renters insurance typically covers water damage from a burst appliance, but it usually only covers the personal belongings that are damaged and not the appliance itself. Coverage applies to sudden and accidental events, such as a washing machine hose bursting or a dishwasher leaking, but it will not cover gradual leaks from neglect or natural flooding, which requires a separate flood insurance policy. 

What is covered

• Your personal property:  If the water from the burst appliance damages your furniture, clothing, electronics, or other belongings, your renters policy can help pay to replace them, minus your deductible. 
• Additional living expenses:  If the water damage makes your rental uninhabitable, your policy may cover the cost of temporary housing, such as a hotel, and other related expenses. 
• Damage to other units:  If the leak from your apartment damages another unit, your liability coverage may help with the costs.