That the laptop shuts down immediately even though 60% is displayed means the chance of a battery defect is very high, or:
a hardware problem
the percentage display is very likely incorrect
safety shutdown inside the battery protection circuit or a charge thresholds
firmware or a software/OS problem
BIOS, ACPI, Drivers, other tools, etc..
calibration problem
Battery health Excellent only indicates the level of wear, not whether the battery can actually deliver power, in most cases.
Many laptops (ThinkPads, ASUS, Dell, etc.) have charge thresholds, e.g. stopping at 60%, which can be set via the BIOS, ACPI, or other tools.
A complete discharge / recalibration cycle plus a BIOS reset may help.
1. Let the battery drain completely until it reaches 0%.
2. Then remove the battery and start the laptop without it, and reset the BIOS. After that, insert the battery again and start the system with both the battery and the power cable connected, and check whether it can charge to 100%.
3. If it gets stuck again at 60%, repeat steps 1 and 2 After that, if possible, try booting a live OS with the battery and power cable connected and see whether it can charge to 100%.
If this is still not possible, the battery has likely developed some kind of lock or defect or the issue is likely related to the firmware, such as the battery controller, embedded controller, or BIOS/UEFI
If the battery charges in the live OS, you have a software / OS problem
If it does not charge there either, you have a hardware problem
Check whether anything from these posts can help you further.
At our company, I could check this much faster because we often have the same model multiple times. I would simply take a battery from another laptop to test it, and also put the supposedly defective battery into a different machine to see what happens