From looking at BF-21361, WiredTiger is opening an excessive amount of files, reaching almost 64K open files. The recommended machine file limit is 64K.
here.
The error seems to be failing from:

    /* Create/Open the file. */
    WT_SYSCALL_RETRY(((pfh->fd = open(name, f, mode)) == -1 ? -1 : 0), ret);
    if (ret != 0)
        WT_ERR_MSG(session, ret,
          pfh->direct_io ? "%s: handle-open: open: failed with direct I/O configured, some "
                           "filesystem types do not support direct I/O" :
                           "%s: handle-open: open",
          name);

Looking at the FTDC data:

• This shows that dhandles are not being discarded, when verify calls are occurring, eventually reaching to a point where the machine's limit is reached.
• This bug could potentially be occurring, from the dhandle not being able to be cleaned in it's interaction with session verify.
• I have verified that session verify itself does not open any new dhandles through tracking the statistics.
• Through the ss wt cache bytes read into cache metric, it also conveys that verify is reading in a lot of bytes, which is expected.
• We also require the dhandle, checkpoint and schema lock from verify.

Investigation:

• Understand the interaction between how dhandle interacts with verify
• Investigate why the dhandle write lock is being acquired.
• Look at possible reasons why the old dhandle's are not being sweeped