There has been much written about this topic, most of it from students of philosophy. One example is from Harvard University (The Power of Forgiveness, 2021) which discusses the REACH program and how forgiving someone lifts the burden from the offended. There are all kinds of ways to lift your burden through forgiving others.
We are to forgive as we have been forgiven (Matt 6.12).
If we forgive, our Father will forgive us, but if we do not forgive our Father will not forgive us (Matt 6.14-15).
I always understood forgiving another as a command. If I am to be holy as my Father is Holy, then I will do as He does.
From the very beginning He showed us how important forgiveness is when He forgave Adam and Eve. Though the word is not there the concept and understanding is. We find that throughout Scripture the Father stands ready to forgive. We need to ask for it, and repent of our sin. Jeremiah 31.18 seems to connect repentance with remorse.
In Gen 4.6-7 we find God asking Kayin why he is angry and downcast, or his countenance has fallen. Then He says that if Kayin does good, he will be able to hold his head high, or words to that effect.
The Hebrew text says if he improves himself, "you will be forgiven." Exodus 34.7 states God forgives iniquity. The word used in Genesis is related to the word used in Exodus. Why the English does not show this is disturbing. For holding one's head high is different from being forgiven though the results are similar.
What we do see is that contrary to the teaching of philosophy and psychology forgiving seems to have nothing to do with the forgiver, but everything to do with the forgiven. I cannot agree for a minute that Yeshua had His burden lifted by forgiving us: it was our burden lifted up - the offender's burden. God's nature is to forgive those who desire His forgiveness. My burden was lifted when He forgave. I may carry a self-imposed burden of constantly remembering the offense someone did to me, but that has nothing to do with forgiving another.
Joseph b. Abba Mari ibn Kaspa (1280-1340) says this regarding Kayin's complaint when told he was to be a wanderer and "Is my iniquity too great to be borne?" (verse 13), "Forgiving iniquity for the one who forgives, 'lifts up' the transgressions from the sinner and lightens his burden, figuratively bearing it for him."
The Hebrew word used for forgive means to lift up, to forgive.
Do we get that? Forgiving someone is a command, but it has nothing to do with me and all about them. My desire should be to forgive, not for my satisfaction or betterment, but to lighten their load. When asked by someone to forgive them, my response is that has already been done. The opposite is true: Failure to forgive a person means you increase their burden, make their yoke heavier. No wonder God says He will not forgive us if we don't forgive others.