Total logical reads per database on SQL Server
You could use a query like this, with the caveat that it will also track backup activity as reads. I'm also not aware of a DMV that tracks logical reads in the way you want.
To account for the backups caveat, you may want to stick it in an Agent Job and log it to a table at the beginning and end of working periods, or some other cadence that makes sense.
If you have Query Store enabled on all of your databases, you could take a daily snapshot of runtime_stats to get closer to the truth. But that's a big if, and depending on your settings it may not capture all query activity.
SELECT
    run_date = 
        GETDATE(),
    days_up = 
        DATEDIFF
        (
            DAY,
            DATEADD
            (
                MILLISECOND,
                -vfs.sample_ms,
                GETDATE()
            ),
            GETDATE()
        ),
    database_name = 
        DB_NAME(vfs.database_id),
    drive = 
        LEFT
        (
            mf.physical_name, 
            1
        ),
    mf.physical_name,
    size_on_disk_mb = 
        vfs.size_on_disk_bytes / 1024 / 1024.,
    read_latency = 
        (vfs.io_stall_read_ms 
            / NULLIF(vfs.num_of_reads, 0)),
    mb_read = 
        vfs.num_of_bytes_read 
            / 1000000.,
    avg_mb_per_read =     
        (vfs.num_of_bytes_read 
            / NULLIF(vfs.num_of_reads, 0)) / 1000000.,
    avg_read_stall = 
        vfs.num_of_reads 
            / NULLIF(vfs.io_stall_read_ms, 0),
    write_latency = 
        (vfs.io_stall_write_ms 
            / NULLIF(vfs.num_of_writes, 0)),
    mb_written =
        vfs.num_of_bytes_written / 1000000.,
   avg_mb_per_write = 
       (vfs.num_of_bytes_written 
           / NULLIF(vfs.num_of_writes, 0)) / 1000000.,
    avg_write_stall = 
        vfs.num_of_writes
            / NULLIF(vfs.io_stall_write_ms, 0)
FROM sys.dm_io_virtual_file_stats(NULL, NULL) AS vfs
JOIN sys.master_files AS mf
    ON  vfs.database_id = mf.database_id
    AND vfs.file_id = mf.file_id
ORDER BY size_on_disk_mb DESC;