As per this page:
The SonicWALL Packet Monitor feature allows you to capture and examine
network traffic as it crosses your firewall. When activated,
Packet Monitor logs the details of packets as they pass through the
device, recording data such as the packet's origin, destination and
port number. This in turn can help you to gain information about the
conditions on your network and identify potential threats.
Given that you're using a layer 2 switch I'd say the two PCs your pinging between are on different layer 3 networks and therefore need to send their data to the SonicWall which is then performing the routing between the networks and monitoring the traffic at the same time.
I found the issue, it has to do with the device itself, specifically an Meraki MR42 AP. When the 802.03at Meraki APs first powers up, it does so in 802.03af mode, thus limiting the power it can draw. Then later in the boot sequence it tries to request more power to be delivered, and for some reason the HP switches does not understand to give it the full 33 watts it needs. The solution is to force the port to allocate power based on a configured value instead of what's negotiated over LLDP. The Meraki documentation shows you how to do it through the GUI, which in my book isn't that useful. Instead, the following commands does the exact thing but for several ports at once.
interface [port_range] poe-value 33
interface [port_range] poe-allocate-by value
interface [port_range] power-over-ethernet critical
The first command sets the "value" for the port to 33W, maximum under the IEEE 802.03at standard.
The second command forces the port to forget about LLDP and just give the device connected to the port whatever it chooses to consume, instead of limiting it.
The third command is probably not necessary, all it should do is to list the port as "critical", aka. tell the switch to shut something else down if it experiences shortage of available PoE power, but I left it in as Cisco Meraki specifically listed it in their fix.
The most amusing thing is that the APs doesn't actually draw any more power after this, at least when they are on standby with no connected clients, but they probably operate better at higher loads, and you get rid of that annoying error in the Meraki dashboard.
https://documentation.meraki.com/MR/Monitoring_and_Reporting/MR34_Operates_in_Low_Power_Mode_on_HP_ProCurve_Switch
Best Answer
It rather depends on what is real. 24V 6.5W is not 24V 0.5 A - but I think the latter number is just what the default (passive) POE power brick is, and they are oversized somewhat by default.
24V 0.5A would be 12W. 24 of those would be 288W and require the 500W switch.
6.5W X 24 ports would be 156W and the 250W would be fine.
Actual data update - not having the time free to muck up my network for this pro bono question, I checked the POE-Brick input against my Kill-A-Watt, and got a peak actual draw of (drumroll, please) 4 Watts (even with the radios blasting away on high power, which is not how I normally run them.)
VA is a bit worse at 8, but that's just the poor 120VAC power factor into a lightly-loaded 12 Watt AC/DC power supply. So, whatever inefficency is involved in the power brick and the draw of the radio is 4 watts or less (observed.) Call it 4.499 if you like, or call it 5 - regardless, this would appear to confirm the 6.5W worst case maximum draw as a very reasonable specification. To the original question, this means that 23 or 24 APs would be easily powered from a 250 watt (24V passive) POE switch.
If 802.3 af/at is something the OP is more comfortable with, the (slightly more expensive) UAP-AC-Pro model is of that 48V POE flavor, but it has a maximum draw spec of 9W, which likely means that a 250W POE switch will not be able to run 23-24 of them, since the Watt rating of POE switches seems to typically include the power needed to run the switch itself.