Ensure that your network devices (routers, switches, access points) are running the latest firmware updates. Sometimes, firmware updates address compatibility and communication issues.

make sure your printer is running the latest firmware available. This can sometimes resolve compatibility issues with newer devices or protocols.

While allowing communication between networks is important, security practices might involve isolating different network segments.

Use network monitoring tools to inspect network traffic and identify any patterns that might be causing the communication issue.

it might be helpful to consult the documentation for your printer, networking equipment, and any relevant application control settings.

It seems like you've taken the right steps in allowing communication from the DMZ network (192.168.8.0/24) to the LAN network (10.8.8.0/25) where your HP printer is located. Since you've confirmed that you can access the printer's web portal and ping its IP address from your iPhone on the DMZ network, the issue might be related to AirPrint setup or network discovery.

You're encountering difficulty printing from devices in your DMZ (192.168.8.0/24) to a printer in your LAN zone (10.8.8.0/25), despite configuring an "Application Control" rule to allow communication. To address this, first verify that your firewall rules are permitting the necessary protocols and ports, such as those used by AirPrint (e.g., Bonjour on port 5353). Confirm that your HP printer supports AirPrint and is set up to accept print jobs from the DMZ. Since AirPrint uses mDNS and Bonjour, ensure these services can cross between DMZ and LAN. While adjusting settings, also maintain proper network security. Check the stability of your iPhone's connectivity between DMZ and LAN, and consider updating firmware/software. If challenges persist, consult network logs for insights or explore alternative methods like a print server.

pls confirm your wifi in isolation mode is disable an airprint is enable

Given that you've ensured proper network connectivity between your DMZ network (192.168.8.0/24) and the LAN network (10.8.8.0/25) where your HP printer resides and verified access to the printer's web portal and successful pinging from your iPhone within the DMZ network, the issue at hand may likely pertain to AirPrint configuration or network discovery. To address this, first, ensure that your HP printer supports AirPrint and is correctly configured for it. Validate that Bonjour (mDNS) protocol communication is functioning across the networks without any firewall obstructions, as AirPrint relies on this for device detection. Review and adjust firewall rules as necessary, permitting the required ports and protocols for AirPrint. Additionally, cross-check network settings, verify the printer's alignment with the LAN subnet (10.8.8.0/25), and ensure your iPhone is connected to the DMZ network with a strong Wi-Fi signal. Exploring these factors will help diagnose and resolve the AirPrint connectivity issue effectively.

Employ network monitoring utilities to examine network traffic and detect any patterns that could be contributing to the communication problem.