Currently we don't have a way to get insight into Postgres connections
being exhausted.

By using the prometheus' [`DBStats`
collector](https://github.com/prometheus/client_golang/blob/main/prometheus/collectors/dbstats_collector.go),
we get some insight out-of-the-box.

```
# HELP go_sql_idle_connections The number of idle connections.
# TYPE go_sql_idle_connections gauge
go_sql_idle_connections{db_name="coder"} 1
# HELP go_sql_in_use_connections The number of connections currently in use.
# TYPE go_sql_in_use_connections gauge
go_sql_in_use_connections{db_name="coder"} 2
# HELP go_sql_max_idle_closed_total The total number of connections closed due to SetMaxIdleConns.
# TYPE go_sql_max_idle_closed_total counter
go_sql_max_idle_closed_total{db_name="coder"} 112
# HELP go_sql_max_idle_time_closed_total The total number of connections closed due to SetConnMaxIdleTime.
# TYPE go_sql_max_idle_time_closed_total counter
go_sql_max_idle_time_closed_total{db_name="coder"} 0
# HELP go_sql_max_lifetime_closed_total The total number of connections closed due to SetConnMaxLifetime.
# TYPE go_sql_max_lifetime_closed_total counter
go_sql_max_lifetime_closed_total{db_name="coder"} 0
# HELP go_sql_max_open_connections Maximum number of open connections to the database.
# TYPE go_sql_max_open_connections gauge
go_sql_max_open_connections{db_name="coder"} 10
# HELP go_sql_open_connections The number of established connections both in use and idle.
# TYPE go_sql_open_connections gauge
go_sql_open_connections{db_name="coder"} 3
# HELP go_sql_wait_count_total The total number of connections waited for.
# TYPE go_sql_wait_count_total counter
go_sql_wait_count_total{db_name="coder"} 28
# HELP go_sql_wait_duration_seconds_total The total time blocked waiting for a new connection.
# TYPE go_sql_wait_duration_seconds_total counter
go_sql_wait_duration_seconds_total{db_name="coder"} 0.086936235
```

`go_sql_wait_count_total` is the metric I'm most interested in gaining,
but the others are also very useful.

Changing the prefix is easy (`prometheus.WrapRegistererWithPrefix`), but
getting rid of the `go_` segment is not quite so easy. I've kept the
changeset small for now.

**NOTE:** I imported a library to determine the database name from the
given conn string. It's [not as
simple](https://www.postgresql.org/docs/current/libpq-connect.html#LIBPQ-CONNSTRING)
as one might hope. The database name is used for the `db_name` label.

---------

Signed-off-by: Danny Kopping <dannykopping@gmail.com>