First, "my soul" is very common phrase in the Hebrew (in this case quoting Hab 2:4) and according to BDAG #2 has the meaning of the person or inner human life. This is why most version render Heb 10:38 (and usually correspondingly Hab 2:4) with a personal pronoun giving something like, "I take no pleasure in him" (eg, NIV, NLT, BSB, CSB, GNB, etc). The other render it more literally.
The phrase "my soul" is common in the OT and usually means "me" or "self" or "myself" or even "I", etc, as the inner seat of emotions: see Luke 12:19 "And I'll say to myself, 'You have plenty of grain laid up for many years … '" (NIV); "And I will say to my soul, 'Soul, you have ample goods laid up for many years … '" (ESV).
For example in the OT:
- Ps 43:5 - Why, my soul, are you downcast? Why so disturbed within me?
- Psalm 104:1 - Praise the LORD, my soul. (see also v35, Ps 146:1, 103:1, 22, Luke 1:46, etc)
- Psalm 42:11 - Why, my soul, are you downcast?
- Psalm 84:2 - My soul yearns, even faints, for the courts of the LORD
- Ps 31:7 - I will be glad and rejoice in your love, for you saw my affliction and knew the anguish of my soul.
- Ps 31:9 - my eyes grow weak with sorrow, my soul and body with grief.
- Ps 62:1 - Truly my soul finds rest in God;
- Ps 62:5 - Yes, my soul, find rest in God; my hope comes from him.
- Isa 26:9 - My soul yearns for you in the night; in the morning my spirit longs for you.
- Isa 42:1 - Here is My Servant, whom I uphold, My Chosen One, in whom My soul delights. (This is quoted in matt 12:18)
- Jer 32:41 - I will rejoice in doing them good and will assuredly plant them in this land with all my heart and soul.
See also Matt 26:38, Mark 14:34, John 12:27 where Jesus uses the same phrase.
Hab 2:4 Isa 42:1, and Jer 32:41 are interesting as God is speaking and uses the phrase "my soul" (in one place "my heart"). I assume that this is simply the way Hebrews talked and God uses similar phraseology. Therefore, it is possible to call this an anthropomorphism, if one prefers.