I'm able to reproduce the issue here.
Running PostgreSQL manually:
$ sudo sh -c 'cd /etc/runit/sv/postgresql/ && exec sh -x ./run'
+ [ -r conf ]
+ . ./conf
+ PGROOT=/var/lib/postgres
+ PGLOG=/var/log/postgresql.log
+ INITOPTS=-A peer --auth-host=md5 --auth-local=peer --locale en_US.UTF-8
+ : /var/lib/postgres/data
+ [ /var/lib/postgres != /var/lib/postgres ]
+ [ ! -d /var/lib/postgres/data ]
+ exec chpst -u postgres:postgres postgres -D /var/lib/postgres/data
2021-07-10 10:50:41.123 -03 [20760] LOG: starting PostgreSQL 13.3 on x86_64-pc-linux-gnu, compiled by gcc (GCC) 11.1.0, 64-bit
2021-07-10 10:50:41.124 -03 [20760] LOG: listening on IPv6 address "::1", port 5432
2021-07-10 10:50:41.124 -03 [20760] LOG: listening on IPv4 address "127.0.0.1", port 5432
2021-07-10 10:50:41.175 -03 [20760] FATAL: could not create lock file "/run/postgresql/.s.PGSQL.5432.lock": No such file or directory
2021-07-10 10:50:41.180 -03 [20760] LOG: database system is shut down
I then added the following line to the end of the conf in /etc/runit/sv/postgresql/conf so it'd create the folder it's complaining about not existing:
mkdir -p /run/postgresql/ && chown postgres:postgres /run/postgresql
Now it starts successfully here (both from sv start and manually).
sudo sh -c 'cd /etc/runit/sv/postgresql/ && exec sh -x ./run'
+ [ -r conf ]
+ . ./conf
+ PGROOT=/var/lib/postgres
+ PGLOG=/var/log/postgresql.log
+ INITOPTS=-A peer --auth-host=md5 --auth-local=peer --locale en_US.UTF-8
+ mkdir -p /run/postgresql/
+ chown postgres:postgres /run/postgresql
+ : /var/lib/postgres/data
+ [ /var/lib/postgres != /var/lib/postgres ]
+ [ ! -d /var/lib/postgres/data ]
+ exec chpst -u postgres:postgres postgres -D /var/lib/postgres/data
2021-07-10 10:55:12.549 -03 [22164] LOG: starting PostgreSQL 13.3 on x86_64-pc-linux-gnu, compiled by gcc (GCC) 11.1.0, 64-bit
2021-07-10 10:55:12.549 -03 [22164] LOG: listening on IPv6 address "::1", port 5432
2021-07-10 10:55:12.549 -03 [22164] LOG: listening on IPv4 address "127.0.0.1", port 5432
2021-07-10 10:55:12.990 -03 [22164] LOG: listening on Unix socket "/run/postgresql/.s.PGSQL.5432"
2021-07-10 10:55:13.205 -03 [22170] LOG: database system was shut down at 2021-07-10 10:54:32 -03
2021-07-10 10:55:13.269 -03 [22164] LOG: database system is ready to accept connections