I agree with this, I am just adding a few examples here springboarding off your post here
Concerning Peter feeding his sheep, it says back in Jeremiah
Jerm 3:15 And
I will give you pastors according to mine heart,
which shall feed you with knowledge and understanding.
These would give them to understand things, for example Paul
1 Cr 12:3
Wherefore I give you to understand, that no man speaking by the Spirit of God calleth Jesus accursed:
and that no man can say that Jesus is the Lord, but by the Holy Ghost.
As Jesus told Peter to feed his sheep he encourages others to take the oversight of the same as well
1Peter 5:2
Feed the flock of God which is among you,
taking the oversight thereof, not by constraint, but willingly; not for filthy lucre, but of a ready mind (See also Acts 20:28)
These also seem comparable, as far as looking after others, that they might know the state of a flock or persons
Proverbs 27:23
Be thou diligent to know the state of thy flocks, and look well to thy herds.
Similary shown in Paul towards them
Phil 2:19 But
I trust in the Lord Jesus to send Timotheus shortly unto you, that I also may be of good comfort,
when I know your state.
That Paul himself might be in good comfort (concerning them)
or not find them as such as he would
fFor example here
2Cr 12:20 For
I fear, lest, when I come, I shall not find you such as I would, and
that I shall be found unto you such as ye would not: lest there be debates, envyings, wraths, strifes, backbitings, whisperings, swellings, tumults (which is a sorry state)
2Cr 12:21
And lest, when I come again, my God will humble me among you,
and that I shall bewail many which have sinned already, and h
ave not repented of the uncleanness and fornication and lasciviousness which they have committed.
Seems one house would look after and report on what is going on in the other house and Paul would chime in
1Cr 1:11 For
it hath been declared unto me of you, my brethren,
by them which are of the house of C

e,
that there are contentions among you.
Just a few places that agree in feeding them with understanding, taking oversight, looking after their state in all those ways.