MySQL Master-Replica incremental backups (no replies)

I have a client who had me create a Mysql 8.0.35 row-based (not gtid) replication setup. They want the following:

MySQL -
15 minute transaction logs
Nightly incrementals
Weekly fulls

Should I "cp" replica binary logs or use mysqlbinlog (syntax ?) ?

Currently, I am running mysqldump backups every hour on the Replica.

date=$(date +%Y-%m-%d-%H.%M.%S)
/usr/bin/mysql --vertical -e "SHOW REPLICA STATUS" \
| egrep 'Relay_Source_Log_File|Exec_Source_Log_Pos' > /mnt/sql_backups/all-databases_dumpall_02_replica_status_logfile_pos_$(date +%Y-%m-%d-%H.%M.%S).txt
/usr/bin/mysqladmin stop-replica
/usr/bin/mysqldump --all-databases > /mnt/sql_backups/all-databases_dumpall_02_$(date +%Y-%m-%d-%H.%M.%S).sql
/usr/bin/mysqladmin start-replica