Kōzuki was promoted to the first team of J2 League club Kyoto Sanga in 2018.
[3] On 26 August 2022, Kōzuki agreed to join Bundesliga side Schalke 04, where he was initially assigned to the reserve team.
[4] However, following his performances in the Regionalliga West, in December of the same year the Japanese player was promoted to the first team and signed his first professional contract in the process, by penning a deal until 2025, with an option for an automatic extension based on a certain number of appearances.
[6] On 30 January 2024, Kōzuki moved on loan to Górnik Zabrze in Poland until the end of 2024, with an option to buy.
[8] Kōzuki has represented Japan at various youth international levels, having played for all the national teams from the under-16 to the under-19 setup.