Dirty pages

Wireshark watches network traffic.

If your system has a local hard drive or solid-state drive, at least some of the dirty pages are backed by "swap space" (a swap partition or a swap file/paging file/whatever the OS calls it) that's on the local drive, so if those pages are written to the backing store, that doesn't involve any network traffic, so Wireshark won't see it.

Even if you happen to be paging to a file over the network, dirty pages won't show up in the network traffic until the system needs to write them to the backing store.

Therefore, Wireshark is not the right tool to use to determine how many dirty pages are in main memory. You should use whatever tools your operating system provides for this, if any. Different operating systems may provide different tools, although some of the "free software" desktop environments might have portable GUI tools that can use the operating-system-dependent APIs on Linux/*BSD/Solaris/etc. to find a free-page count.