To what extent is the truth that 2+2=4 an interpersonal one? Is this because if we had different ideas about it, it would be less true -- that the 'truth' of addition stems from the fact that we all seem to agree on the way it works?

For myself, I would be reluctant to adopt a concept of mathematical truth that relies on community agreement, but I am curious as to why you emphasize the role of more than one person.

The interpersonal aspect is in there to constrain what the symbols in "2+2=4" actually mean; it has no bearing on the underlying logical truth (part 2). Nevertheless, common agreement in the use of terms is necessary to give those terms meaning. In that respect, the opinions of other people do impact whether such a statement evaluates to "true". For the same reason, the isolated statement "2+2=6" should evaluate to "false", even though someone could say, "oh no, see, here, I meant this '6' symbol to mean '4'." That person may have an accurate internal model of reality, but hasn't correctly conveyed it.

Words can be wrong in terms of sudden unexplained deviation from common usage.