feat: make database connection pool size configurable (#21403)

Closes https://github.com/coder/coder/issues/21360

A few considerations/notes:
- I've kept the number of conns to 10 in all other places, except coderd
- which uses the config value
- I opted to also make idle conns configurable; the greater the delta
between max open and max idle, the more connection churn
- Postgres maintains a [_process_ per
connection](https://www.postgresql.org/docs/current/connect-estab.html),
contrary to what the comment said previously
- Operators should be able to tune this, since process churn can
negatively affect OS scheduling
- I've set the value to `"auto"` by default so it's not another knob one
_has to_ twiddle, and sets max idle = max conns / 3

---------

Signed-off-by: Danny Kopping <danny@coder.com>

site/src/api/typesGenerated.ts

@@ -1736,6 +1736,8 @@ export interface DeploymentValues {
 	readonly ephemeral_deployment?: boolean;
 	readonly pg_connection_url?: string;
 	readonly pg_auth?: string;
+	readonly pg_conn_max_open?: number;
+	readonly pg_conn_max_idle?: string;
 	readonly oauth2?: OAuth2Config;
 	readonly oidc?: OIDCConfig;
 	readonly telemetry?: TelemetryConfig;
@@ -3450,6 +3452,13 @@ export type PostgresAuth = "awsiamrds" | "password";
 
 export const PostgresAuths: PostgresAuth[] = ["awsiamrds", "password"];
 
+// From codersdk/deployment.go
+/**
+ * PostgresConnMaxIdleAuto is the value for auto-computing max idle connections
+ * based on max open connections.
+ */
+export const PostgresConnMaxIdleAuto = "auto";
+
 // From codersdk/deployment.go
 export interface PprofConfig {
 	readonly enable: boolean;