To experience suffering is to configure one's self to / with Christ
... already in the act of Baptism, which brings about a configuration with Christ, and then through his Sacrifice...the Church is continually being built up spiritually as the Body of Christ. In this Body, Christ wishes to be united with every individual, and in a special way he is united with those who suffer. (Salvifici Doloris, 24)
While this answer begins with what I was taught by a Catholic deacon some years ago, on a more biblical basis you will find in Collosians a complete embracing of suffering
1 Collosians 23, 24,
Now I rejoice in my sufferings for your sake, and in my flesh I am filling up what is lacking in the afflictions of Christ on behalf of his body, which is the church,
One of the themes that the Catholics teach is that our suffering configures us with Christ, who suffered on the Cross for all of our sins. There is an extended meditation here in Salvifici Doloris covering the Christian meaning of human suffering. Pope St. John Paul II observes that
... we recall the truth expressed in the Encyclical Redemptor
Hominis: in Christ "every man becomes the way for the Church." It can
be said that man in a special fashion becomes the way for the Church
when suffering enters his life. This happens, as we know, at different
moments in life, it takes place in different ways, it assumes
different dimensions; nevertheless, in whatever form, suffering seems
to be, and is, almost inseparable from man's earthly existence.
That's one take of many on the topic of suffering.
You ask "does God feel and appreciate the resiliency of our suffering?"
I answer: Yes. God is with us always.
John 14: 16- 17 (NAB)
And I will ask the Father, and he will give you another Advocate 8 to
be with you always, the Spirit of truth, which the world cannot
accept, because it neither sees nor knows it. But you know it, because
it remains with you, and will be in you.
Under the basis of the trinitarian Godhead, the Son felt mankind's suffering on the Cross. Because the Father and the Son are one -
John 10: 30
The Father and I are one."
... God knows what Jesus feels, what Jesus felt.
What about appreciating the resiliency of our suffering?
The Holy Spirit is sent to us from God to be with us always(see above). Beyond God knowing of our suffering (God knows all) and appreciating our suffering (through the person of Christ and the Cross) the appreciation by God of our suffering is a Christian belief that goes back to the early church; the original Saints were martyrs for Christ.
- This Christian belief, that the saints of the early church, most of whom were Martyrs for the Church (just as Christ was martyred for all of us) and thereby earned the reward of Heaven shows but one example of God appreciating the suffering of individuals. (There have been entire books written on this topic).
From a contemporary Christian point of view ...
... the answer remains Yes. There is a well known poem: Footprints in the Sand by Margaret Fishback Powers
“One night I dreamed a dream. As I was walking along the beach with my
Lord. Across the dark sky flashed scenes from my life. For each scene,
I noticed two sets of footprints in the sand, One belonging to me and
one to my Lord.
After the last scene of my life flashed before me, I looked back at
the footprints in the sand. I noticed that at many times along the
path of my life, especially at the very lowest and saddest times,
there was only one set of footprints.
This really troubled me, so I asked the Lord about it. “Lord, you said
once I decided to follow you, You’d walk with me all the way. But I
noticed that during the saddest and most troublesome times of my life,
there was only one set of footprints. I don’t understand why, when I
needed You the most, You would leave me.”
He whispered, “My precious child, I love you and will never leave you
Never, ever, during your trials and testings. When you saw only one
set of footprints, It was then that I carried you.”
The message here is clear: the personal connection with Christ, who cares for us regardless of our condition, and is another perspective on how God will be with us always. He doesn't just appreciate our suffering, He's there to help when we suffer. That message is pretty clear across multiple Christian denominations.
Another excerpt from that extended meditation on suffering
The Redeemer suffered in place of man and for man. Every man has his
own share in the Redemption. Each one is also called to share in that
suffering through which the Redemption was accomplished. He is called
to share in that suffering through which all human suffering has also
been redeemed. In bringing about the Redemption through suffering,
Christ has also raised human suffering to the level of the Redemption.
Thus each man, in his suffering, can also become a sharer in the
redemptive suffering of Christ.