How to monitor backup and restore progress in SQL Server

There are few tips that might help you to diagnose problems during backup restore on SQL Server 2016+.

Common restore script:

RESTORE DATABASE [mydb] 
FROM  DISK = N'F:\DatabaseBackups\mydb.bak' 
WITH  FILE = 1,  
MOVE N'mydb' TO N'G:\Databases\mydb.mdf',  
MOVE N'mydb_log' TO N'G:\DatabaseLogs\mydb.ldf',  
NOUNLOAD,  STATS = 1

STATS = 1 - for receiving status messages every 1% of progress

The script to validate backup:

RESTORE verifyonly FROM  DISK = N'F:\DatabaseBackups\mydb.bak'

The script to get backup file statistics, it allows to check restored db size:

Restore Filelistonly FROM  DISK = N'F:\DatabaseBackups\mydb.bak'

Concurrent restore/shrink tasks might block your restoring procedure. You can monitor restoring process status by the following SQL:

SELECT session_id as SPID, command, a.text AS Query, start_time, percent_complete, dateadd(second,estimated_completion_time/1000, getdate()) as estimated_completion_time, *
FROM sys.dm_exec_requests r CROSS APPLY sys.dm_exec_sql_text(r.sql_handle) a
WHERE r.command in (
   'BACKUP DATABASE', 'RESTORE DATABASE', 
   'RESTORE HEADERONLY', 'DbccFilesCompact', 'DbccSpaceReclaim')

If you see percent_complete is zero for a log time, you might need to add SQL Server user to Perform Volume Maintenance Tasks security policy via secpol.msc. Check the article:
https://docs.microsoft.com/en-us/sql/relational-databases/databases/database-instant-file-initialization?view=sql-server-ver15

You can check resource consumption with sp_who2 function.
The following script uses a temp table for order/filter operation.

CREATE TABLE #sp_who2 (SPID INT,Status VARCHAR(255),
      Login  VARCHAR(255),HostName  VARCHAR(255),
      BlkBy  VARCHAR(255),DBName  VARCHAR(255),
      Command VARCHAR(255),CPUTime INT,
      DiskIO INT,LastBatch VARCHAR(255),
      ProgramName VARCHAR(255),SPID2 INT,
      REQUESTID INT)
INSERT INTO #sp_who2 EXEC sp_who2
SELECT      *
FROM        #sp_who2
-- Add any filtering of the results here :
--WHERE       SPID = 151
-- Add any sorting of the results here :
ORDER BY    DBName ASC

DROP TABLE #sp_who2