All the display stuff for Kingdom Power 5 and above are likely 1 off because they removed an entire kingdom power level and shifted a bunch of stuff down for the new system, but forgot to adjust the display accordingly. The “silver star” or “empty star” from previous versions meant that what everyone has always called a “five star” kingdom was actually the sixth kingdom power upgrade in previous versions. This upgrade was removed (or, more accurately, the 5th power upgrade, previously called 4* was removed) leaving the first power upgrades to skill bonus as gold/tribute amount/gold/tribute chance/skill bonus where it used to be gold/tribute amount/gold/tribute chance/gold/skill bonus.
During transition/grandfathering, everything at the previous power level 6 (five star) and above was synched to its expected new power level, which is now one power level lower (v3.4 5* = v3.4 power level 6 = v3.5 power level 5 = v3.5 5* = all of these are the point when the +1 skill bonus becomes available). The display seems to still be checking for an internal power >=6 to show an additional point of skill bonus and >=2, >= 4, >=8, and >= 10 to show the respective tribute bonuses from the kingdom view window. Tribute bonuses for pre-power 5 didn’t move in respect to absolute power ranks (they remained at the second and fourth power upgrades for a kingdom, which is now represented as 2* and 4* instead of 1* and 3*), which is why those display correctly - because they didn’t have their respective rewards get shifted down a power level.
The code that hands out the bonuses appears to be working correctly, though I can really only give hard independent confirmation due to observing skill bonuses from kingdoms at exactly Power Level 5, where I do indeed get a display of +1 but have +2.