Found in Pathfinder files, not tested in any other gamemode.
It seems that the Skills tab summary is not being updated on the fly, but only refreshed when the user selects a new filter from the dropdown.
Steps to reproduce
Create a new character
Set all starting stats to 10 (no bonuses)
Purchase a Belt of Giant Strength +2 and equip it
Go to Character sheet and see that Climb modifier is +1
Go to skills tab and see that in the summary on the right, the Climb modifier is still 0 (belt modifier not being accounted for)
Choose "All skills" from the skill tab filter above the summary pane
See that teh Climb modifier is now +1