How to identify cross-database queries in SQL Server
I would set up an Extended Events session to capture lock acquired events and stream the events with the API.

First of all the session:

CREATE EVENT SESSION crossdb ON SERVER 
ADD EVENT sqlserver.lock_acquired(
    SET collect_database_name=(1),collect_resource_description=(1)
    ACTION(
        sqlserver.request_id,sqlserver.session_id,
        sqlserver.sql_text,sqlserver.tsql_frame
    )
    WHERE (
            [package0].[equal_boolean]([sqlserver].[is_system], (0)) -- user SPID
        AND [package0].[equal_uint64]([resource_type], (5)) -- OBJECT
        AND [package0].[not_equal_uint64]([database_id], (32767))  -- resourcedb
        AND [package0].[greater_than_uint64]([database_id], (4)) -- user database
        AND [package0].[greater_than_equal_int64]([object_id], (245575913)) -- user object
        AND (
               [mode] = (1) -- SCH-S
            OR [mode] = (6) -- IS
            OR [mode] = (8) -- IX
            OR [mode] = (3) -- S
            OR [mode] = (5) -- X
        )
        AND [database_name] &lt;&gt; N'distribution'
    )
)
WITH (
    MAX_MEMORY=4096 KB,
    EVENT_RETENTION_MODE=ALLOW_SINGLE_EVENT_LOSS,
    MAX_DISPATCH_LATENCY=30 SECONDS,
    MAX_EVENT_SIZE=0 KB,
    MEMORY_PARTITION_MODE=NONE,
    TRACK_CAUSALITY=OFF,
    STARTUP_STATE=OFF
)
GO


Then, you could group the events on transaction_id and tsql_frame. The groups that touch more than one database_id are the ones that issue cross-database statements. You can then extract the statement from the sql_text action, using the offsetStart and offsetEnd from tsql_frame.



I have a similar example on my blog here: https://spaghettidba.com/2015/04/20/tracking-table-usage-and-identifying-unused-objects/