That sounds exactly like the battery calibration issue that was so common on older firmware. Nintendo has official instructions to solve it that you can try, which involves completely charging and discharging the battery several times.The battery percentage indicator would go down 1% like every 3-4 seconds until it drops down to 1%, where it can last around 2 hours before hitting 0%.
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I'm considering ordering one from this link: https://www.ifixit.com/Store/Game-C...OxEke0KwU74ccf1mfSKesBFaNcQpu-mBoC6HkQAvD_BwE
Total is $46 after shipping and taxes.
https://en-americas-support.nintend...-indicator-or-percentage-displays-incorrectly
It's worth a try.