It seems like you already tried to mitigate this problem with the chmod but maybe a chown postgres:postgres is missing
chmod: changing permissions of '/var/run/postgresql': Read-only file system
PostgreSQL Database directory appears to contain a database; Skipping initialization
2024-10-04 06:53:19.047 UTC [1] LOG: starting PostgreSQL 16.1 (Debian 16.1-1.pgdg120+1) on x86_64-pc-linux-gnu, compiled by gcc (Debian 12.2.0-14) 12.2.0, 64-bit
2024-10-04 06:53:19.047 UTC [1] LOG: listening on IPv4 address "0.0.0.0", port 5432
2024-10-04 06:53:19.047 UTC [1] LOG: listening on IPv6 address "::", port 5432
2024-10-04 06:53:19.069 UTC [1] FATAL: could not create lock file "/var/run/postgresql/.s.PGSQL.5432.lock": Read-only file system
2024-10-04 06:53:19.070 UTC [1] LOG: database system is shut down
It seems like you already tried to mitigate this problem with the
chmod
but maybe achown postgres:postgres
is missing