@A-AIC thanks for getting in touch. The information you have been provided is correct. In order to make batteries fit in ultra thin slim chassis they no longer have plastic cases or metal spines surrounding them. This is seen across all manufacturers, not just Dell.
Batteries by design will swell up when they are reaching the end of their life and a result of this can be cracked plastics in areas that surround the batteries. For systems with warranties over 3 years, batteries are not covered for years 4 and 5. This is similar to the standard offering of a 1yr battery warranty and optional 3yr battery. I do not recall anyone offering a battery warranty greater than 3 years from initial purchase.
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You might want to check your country for specific consumer protection laws. I recently took Dell to our protection body in NSW and won - almost identical scenario to yours - battery initially replaced 14 months ago in Precision when it was covered under warranty - same problem happened two weeks after warranty expired.
Dell would not cover it - went to our consumer protection body - essentially the product is not fit for purpose - a laptop is designed for more than a 3 year lifetime and it is not reasonable to replace a battery to only have it fail in exactly the same way in a little more than 12 months.
Dell caved and replaced it and the trackpad for free