In the main postgres configuration file, postgresql.conf, you could set log_min_duration_statement to some value larger than zero. The value is expressed in milliseconds, so for instance setting it to 1000 makes the server log all SQL statements that take longer than 1 second. It may or may not fit your case. (You'd also need some process monitoring that log, I guess.)

The default setting of this parameter is -1 (=disabled):

log_min_duration_statement = -1    # -1 is disabled, 0 logs all statem
+ents
                    # and their durations, > 0 logs only
                    # statements running at least this number
                    # of milliseconds
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And, by the way, you don't need to run "EXPLAIN" queries manually. EXPLAIN has nice machine-readable output formats like json and yaml. For example:

echo "
create table t(n integer primary key);
insert into t select * from generate_series(1,10000);
analyze t;  --> gather table statistics

explain (analyze, verbose, format yaml) select count(*) from t where n
+ between 10 and 20;
" | psql -qtAX
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The output:

- Plan:
    Node Type: "Aggregate"
    Strategy: "Plain"
    Partial Mode: "Simple"
    Parallel Aware: false
    Startup Cost: 8.51
    Total Cost: 8.52
    Plan Rows: 1
    Plan Width: 8
    Actual Startup Time: 0.040
    Actual Total Time: 0.040
    Actual Rows: 1
    Actual Loops: 1
    Output:
      - "count(*)"
    Plans:
      - Node Type: "Index Only Scan"
        Parent Relationship: "Outer"
        Parallel Aware: false
        Scan Direction: "Forward"
        Index Name: "t_pkey"
        Relation Name: "t"
        Schema: "public"
        Alias: "t"
        Startup Cost: 0.29
        Total Cost: 8.48
        Plan Rows: 10
        Plan Width: 0
        Actual Startup Time: 0.022
        Actual Total Time: 0.029
        Actual Rows: 11
        Actual Loops: 1
        Output:
          - "n"
        Index Cond: "((t.n >= 10) AND (t.n <= 20))"
        Rows Removed by Index Recheck: 0
        Heap Fetches: 11
  Planning Time: 0.481
  Triggers:
  Execution Time: 0.149
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