Two control signals one GPIO

so with the pull-ups that's that status of your pins

LOW HIGH
CHRG Charging Not Charging
STDBY Complete Not Complete

You want to detect whether charging is taking place and if the battery is fully charged.

Another way to represent this is

CHRG STDBY state
LOW LOW impossible (can't be both charging and complete)
LOW HIGH Charging, not fully charged
HIGH LOW Not Charging, fully charged
HIGH HIGH impossible (can't be both not charging and not complete)

so if the components can never be in the impossible situation then just looking at one of them you'll know what's the status.

eg if CHRG is LOW then you know it's Charging, not fully charged and if CHRG is HIGH then you know it's Not Charging which means fully charged

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