The holy spirit mentioned in the verse, which you quoted, is Gabriel. So, Gabriel is the "Holy Spirit" there.
Ruh means Spirit and Quds means Holy.
In case of Jesus, Qur'aan says that he was strengthened with a holy spirit. But that does not mean he was strengthened by Gabriel.
It means Jesus was granted with a noble spirit. In other words, like me, Jesus ah a noble soul.
37. The Lord of the heavens and the earth and what is between them, the Beneficent God, they shall not be able to address Him.
38. The day on which the spirit and the angels shall stand in ranks; they shall not speak except he whom the Beneficent God permits and who speaks the right thing.
The spirit seems to mentioned as something different or distinct from the angels. I've seen all of the instances where spirit and holy spirit are mentioned in the Quran and it kind of seems like a confusing mess where one can't tell what the Quran really means by spirit or even holy spirit. The meaning seems to keep changing. It's kind of weird or almost like the author isn't keeping track of how this termed was used in the past in the Quran and gives it another meaning, then switches the meaning back again.