SQL Server : Deadlock is happening even with small batch size

Question

We have a stored procedure which purges old data. We do the purging on daily basis during off-business hours. Also we do purging in small batches. But in the 5 hour window of purging, we see around 2 deadlocks on a daily basis. Our purging SP is getting deadlocked with an application stored procedure. Below is the deadlock graph:

Deadlock XML:

<deadlock>   
    <victim-list>    
        <victimProcess id="process1ee5a1cca8"/>   
    </victim-list>   
    <process-list>    
        <process id="process1ee5a1cca8" taskpriority="5" logused="37852" waitresource="PAGE: 8:3:33782409 " waittime="1341" ownerId="17013937844" transactionname="batch_archive" lasttranstarted="2021-01-13T00:21:32.883" XDES="0x20e0c8d900" lockMode="U" schedulerid="16" kpid="9320" status="suspended" spid="1029" sbid="0" ecid="0" priority="-5" trancount="2" lastbatchstarted="2021-01-12T22:35:01.590" lastbatchcompleted="2021-01-12T22:35:01.590" lastattention="1900-01-01T00:00:00.590" clientapp="SQLAgent - TSQL JobStep (Job 0xAC6E654BCA73184DA4769BFB133908A1 : Step 2)" hostname="SERVER_NAME" hostpid="4024" loginname="Domain\SQL_SRVC_ACCOUNT" isolationlevel="read committed (2)" xactid="17013937844" currentdb="6" currentdbname="dba_admin" lockTimeout="4294967295" clientoption1="673316896" clientoption2="128056">
            <executionStack>      
                <frame procname="dba_admin.dbo.PURGING_SP" line="695" stmtstart="46958" stmtend="47248" sqlhandle="0x03000600119b6e780e397800aeac000001000000000000000000000000000000000000000000000000000000">  delete from DB_NAME..TABLE_B  where activity_id in      (select activity_id from batch) OPTION(MAXDOP 1    </frame>      
                <frame procname="adhoc" line="8" stmtstart="226" stmtend="626" sqlhandle="0x01000600fa8ab015c0c41e452500000000000000000000000000000000000000000000000000000000000000">  EXEC @return_value = [dbo].[PURGING_SP]    @arch_mon_crit = 93,    @batch_size = 5,    @po_sql_code = @po_sql_code OUTPUT,    @po_sql_msg = @po_sql_msg OUTPU    </frame>     
            </executionStack>     
            <inputbuf>    DECLARE @return_value int,    @po_sql_code int,    @po_sql_msg nvarchar(2000)    set deadlock_priority low;    EXEC @return_value = [dbo].[PURGING_SP]    @arch_mon_crit = 93,    @batch_size = 5,    @po_sql_code = @po_sql_code OUTPUT,    @po_sql_msg = @po_sql_msg OUTPUT    SELECT @po_sql_code as N&apos;@po_sql_code&apos;,    @po_sql_msg as N&apos;@po_sql_msg&apos;    SELECT &apos;Return Value&apos; = @return_value       </inputbuf>
        </process>    
        <process id="process1a77fc4ca8" taskpriority="0" logused="5176" waitresource="OBJECT: 8:1697441121:2 " waittime="7176" ownerId="17013959258" transactionname="user_transaction" lasttranstarted="2021-01-13T00:21:36.213" XDES="0x25455748b0" lockMode="IX" schedulerid="3" kpid="5484" status="suspended" spid="304" sbid="0" ecid="0" priority="0" trancount="2" lastbatchstarted="2021-01-13T00:21:36.213" lastbatchcompleted="2021-01-13T00:21:35.260" lastattention="1900-01-01T00:00:00.260" clientapp="rx-process_temp_jpid[5740]" hostname="APP_SERVER" hostpid="0" loginname="DOMAIN\SRV_ACCOUNT" isolationlevel="read committed (2)" xactid="17013959258" currentdb="8" currentdbname="DB_NAME" lockTimeout="4294967295" clientoption1="673185824" clientoption2="128056">     
            <executionStack>      
                <frame procname="DB_NAME.dbo.APP_SP_INSIDE_MAIN_SP" line="75" stmtstart="2928" stmtend="3252" sqlhandle="0x0300080011c5170b94ab5e01b0a8000001000000000000000000000000000000000000000000000000000000">  INSERT INTO TABLE_A ( email_id ,activity_id ,header ,content ,content_type ) VALUES ( @p_email_id ,@p_activity_id ,@p_header ,@p_content ,@p_content_type    </frame>      
                <frame procname="DB_NAME.dbo.APP_SP" line="301" stmtstart="14314" stmtend="15014" sqlhandle="0x0300080012f6881b97ab5e01b0a8000001000000000000000000000000000000000000000000000000000000">  EXEC @v_ret_value = APP_SP_INSIDE_MAIN_SP @p_email_id , @p_activity_id , @p_alias_id , @p_subject , @p_email_date , @p_email_size , @p_num_attachments , @p_charset , @p_message_id , @p_from_email_address , @p_recv_email_address , @p_delete_flag , @p_header , @p_content , @p_content_type , @p_text_content , @v_sql_code OUTPUT , @v_sql_message OUTPU    </frame>      <frame procname="adhoc" line="1" stmtstart="1202" stmtend="1898" sqlhandle="0x010008009805062a00bed2062300000000000000000000000000000000000000000000000000000000000000">  EXEC @P0 = APP_SP   @P1  ,  @P2  ,  @P3  ,  @P4  ,  @P5  ,  @P6  ,  @P7  ,  @P8  ,  @P9  ,  @P10  ,  @P11  , &apos;n&apos; , @P12  ,  @P13  ,  @P14  ,  @P15  ,  @P16  ,  @P17  ,  @P18  ,  @P19  ,  @P20 OUT  ,  @P21  ,  @P22  ,  @P23  ,  @P24  ,  @P25  ,  @P26  ,  @P27  ,  @P28  ,  @P29  ,  @P30  ,  @P31  ,  @P32  ,  @P33 OUT  ,  @P34 OU    </frame>      <frame procname="unknown" line="1" sqlhandle="0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000">  unknown    </frame>     </executionStack>     <inputbuf>  (@P0 decimal(38,4) OUTPUT,@P1 bigint,@P2 bigint,@P3 nvarchar(4000),@P4 datetime2,@P5 int,@P6 int,@P7 nvarchar(4000),@P8 nvarchar(4000),@P9 nvarchar(4000),@P10 nvarchar(4000),@P11 nvarchar(4000),@P12 nvarchar(4000),@P13 nvarchar(max),@P14 nvarchar(4000),@P15 nvarchar(max),@P16 nvarchar(4000),@P17 nvarchar(4000),@P18 nvarchar(4000),@P19 nvarchar(4000),@P20 decimal(38,4) OUTPUT,@P21 int,@P22 int,@P23 bigint,@P24 bigint,@P25 nvarchar(4000),@P26 bigint,@P27 datetime2,@P28 int,@P29 nvarchar(4000),@P30 nvarchar(4000),@P31 nvarchar(4000),@P32 bigint,@P33 decimal(38,4) OUTPUT,@P34 nvarchar(4000) OUTPUT)EXEC @P0 = APP_SP   @P1  ,  @P2  ,  @P3  ,  @P4  ,  @P5  ,  @P6  ,  @P7  ,  @P8  ,  @P9  ,  @P10  ,  @P11  , &apos;n&apos; , @P12  ,  @P13  ,  @P14  ,  @P15  ,  @P16  ,  @P17  ,  @P18  ,  @P19  ,  @P20 OUT  ,  @P21  ,  @P22  ,  @P23  ,  @P24  ,  @P25  ,  @P26  ,  @P27  ,  @P28  ,  @P29  ,  @P30  ,  @P31  ,  @P32  ,  @P33 OUT  ,  @P34 OUT                                                                            </inputbuf>    
                </process>   
    </process-list>
    <resource-list>    
        <pagelock fileid="3" pageid="33782409" dbid="8" subresource="FULL" objectname="DB_NAME.dbo.TABLE_B" id="lock1ffd963c00" mode="IX" associatedObjectId="72065991888076800">     
            <owner-list>      
                <owner id="process1a77fc4ca8" mode="IX"/>     
            </owner-list>     
            <waiter-list>      
                <waiter id="process1ee5a1cca8" mode="U" requestType="wait"/>     
            </waiter-list>    
        </pagelock>    
        <objectlock lockPartition="2" objid="1697441121" subresource="FULL" dbid="8" objectname="DB_NAME.dbo.TABLE_A" id="lock1bdc26a600" mode="X" associatedObjectId="1697441121">     
            <owner-list>      
                <owner id="process1ee5a1cca8" mode="X"/>     
            </owner-list>     
            <waiter-list>      
                <waiter id="process1a77fc4ca8" mode="IX" requestType="wait"/>     
                </waiter-list>    
        </objectlock>   
    </resource-list>  
</deadlock>  

Few other Important Info:

• Both the tables involved in deadlock (TABLE_A & TABLE_B) are partitioned tables.
• Server is having 16 processors, hence lock partitioning is enabled by default.
• Lock_escalation_desc for both the involved tables in sys.tables is TABLE.
• Table_B is a parent table of Table_A. Since App_SP is doing INSERT whereas PURGING SP is doing DELETE, we cannot have the same sequence in both the SPs because of referential integrity.
• Purging SP is doing DELETE from around 40 tables in a single transaction. We are using loop to delete the data in one go, but one loop will delete data for a very small batch. ONE LOOP = ONE TRANSACTION that purges data from 40 tables.

I need help on below points:

• One year old data is getting deleted whereas a new data is getting inserted. So how can a deadlock happen between them as data is residing at two different places.
• Why object lock is being taken on TABLE_A? We are providing very small batch size, so I don't think lock escalation can happen at entire table level.
• If you see in resource_list of deadlock graph, one of the resource is objectlock lockPartition="2". what does LOCKPARTITION = 2 means? does it mean that partition no = 2 of table is locked? I know it is coming from lock partitioning mechanism but does it causing any negative impact and causing deadlock?

Any help would be appreciated to permanently fix the deadlock.