As for your question, it appears you need to set up VLAN 1003 on your network and configure your DHCP server to access that VLAN, if you want to use the in-built guest network:
https://www.thegeekpub.com/5191/use-airport-extreme-guest-network-bridge-mode/
You’re using getting-rather-old and residential-grade Wi-Fi devices. They were great devices for their time for residential configurations, too. That’s all your choice, of course. But it’s going to limit you.
Your design is also an oddly fragmented network, if I understand the description correctly. Barring some detail omitted from the description (security?), I’d usually switch all of the AirPort devices over to their access point mode (Apple calls this mode “bridged”) offering the same SSID and (if VLANs are in use) on the same VLAN. This allows clients to roam across all parts of the network without having to disconnect and reconnect at each signal transition.
Then I’d add one AP for the guest network, if it was localized to one area.
I’d probably replace all of this with (would would probably be fewer) Ubiquiti LR APs or Wi-Fi 6 APs, and be done with the AirPort devices. Having chased issues with and switched one network from multiple AirPort APs to about a quarter the number of Ubiquiti APs a while back, coverage was far better, and the drop-outs disappeared. Some AirPorts can get flaky. I’ve seen several do random ~fifteen second signal drop-outs, among other weirdnesses.
These days, a Wi-Fi mesh system can be an alternative, if you don’t already have wired backhaul.
And for completeness, you can generate and print a QR code to allow guests to easily access the SSID and password for the Wi-Fi networks, without having to type it in. This is a way to use secure network encryption and a decent password with guests.
