I don't believe there is a specific endpoint that will list the entire set of serial numbers. However, you can get the serial numbers from the slots using a 'util/bash' endpoint and sending a clsh command.
Here is an example of getting the blade serial numbers:
# curl -sku admin:${bigip_pass} https://${BIGIP-MGMT-ADDR}/mgmt/tm/util/bash -X POST -H "Content-Type: application/json" -d "{ \"command\":\"run\", \"utilCmdArgs\":\"-c 'clsh tmsh show sys hardware field-fmt \| awk \\\'/\^sys hardware system-info/,/\^}/ {if(\$1==\\\"host-board-serial-num\\\") print $2}\\\''\"}" | jq .commandResult | xargs echo -e
host-board-serial-num bld012429s
host-board-serial-num bld012451s
The core command is "utilCmdArgs": "-c 'clsh tmsh show sys hardware field-fmt" the rest just gets the specific serial information and dumps it in a more readable format.
Let me know if this gets you closer to what you are looking for.