After replacing tail lights with LED, passenger side running lights are not working

Sometimes LED bulbs have polarity. Try removing that left rear taillight bulbs and then test that voltage again at the right rear.
I do see the right rear taillight wire also splices to and feeds both front running/parking lights, so do the front still work?

A dirty connection could cause a loss of voltage.
If the fronts are working okay, I do not see no need to worry about the left rear then, simply because the splice for it is before the splice for the fronts. So, check the voltage again on that black/yellow wire where it meets up with the other black/yellow wires, the one that feeds the fronts and the one that comes from the multi-function/headlight switch.
Now where exactly this connection or splice is located, the repair manual does not say, so I suggest you just follow the black/yellow wire from the right rear light assembly to find it.
First of all, it appears there is a connection near the right rear light assembly, check the voltage there first before continuing on back toward the light switch.

No, it would not be the bulb, because you have already tested the voltage and 4.5 volts probably is not enough to light the bulb bright enough to see, maybe if it was night time.

Cut? Probably not, since that would usually mean no voltage at all, perhaps broken copper wire strands or maybe a rusted connection.

You are welcome.