Steps to reproduce use case:

1.  Log in as a postgres user and setup env variables (PGDATA, PGLOG, PGPORT etc.), also 
    mkdir $PGDATA/../archive_dir

2.  Create data directory
    initdb -k

3.  Modify postgresql.conf
    wal_level = replica
    archive_mode = on
    archive_command = 'test ! -f /home/postgres/data/pgpro/archive_dir/%f && cp %p /home/postgres/data/pgpro/archive_dir/%f'

4.  Start server
    pg_ctl start -l $PGLOG/logfile

5.  Create example database and run psql
    createdb db_pitr_01
    psql -d db_pitr_1

6.  Create table (just to modify database)
    CREATE TABLE t8x1_float4 AS SELECT random()::float4 as a1 FROM generate_series(1, 8);

7.  Switch to a new WAL file
    SELECT pg_switch_wal();

8.  Make a backup
    pg_basebackup -Ft -X none -D - | gzip > /home/postgres/data/pgpro/db_file_backup.tar.gz

9.  Update table 
    INSERT INTO t8x1_float4 values  (1.);
    INSERT INTO t8x1_float4 values  (2.);
    INSERT INTO t8x1_float4 values  (3.);

10. Switch to a new WAL file
    SELECT pg_switch_wal();

11. Stop database and remove data directory
    pg_ctl stop
    rm -r /home/postgres/data/pgpro/data-debug/*

12. Restore data directory
    tar xvfz db_file_backup.tar.gz -C /home/postgres/data/pgpro/data-debug/

13. Update the following parameters in postgrespro.conf
    recovery_target_time = '2024-03-26 10:26:30 GMT'
    restore_command = 'cp /home/postgres/data/pgpro/archive_dir/%f %p'

14.
   touch recovery.signal

15. 
    pg_ctl start  -l $PGLOG/logfile

16. Start database and see it is in Point In Time Recovery mode
    psql -d db_pitr_01

    db_pitr_01=# SELECT pg_is_in_recovery();
     pg_is_in_recovery 
    -------------------
     t
    (1 row)

    db_pitr_01=# SELECT pg_is_standby_requested();
     pg_is_standby_requested 
    -------------------------
     f
    (1 row)

Now we can differ recovering server in Point In Time Recovery mode from standby mode.
pg_is_standby_requested() returns true for a replica.