When wired headphones are plugged into an iPad they take "precedence" disabling the HomePod use. It's either or usage.
Wireless headphones like AirPods can't play simultaneously alongside a HomePod connection. The only viable option that comes to my mind is to rely on the AirPlay 2 protocol which can keep playing two devices at the same time (multiple AirPlay 2 destinations are possible to choose).
In this case one destination would be your HomePod and the second one would be an AirPlay 2 receiver.
Remember: only AirPlay 2 devices work simultaneously. Regular AirPlay (the first version) doesn't offer this feature.
There're small receivers on the market (by brands like Belkin and WiiM to name just two). They have to be powered (I guess via USB). I'm not aware of a receiver with a wired headphone output, though, so a headphone amplifier should be added to the chain:
iPad -- Wireless --> AirPlay 2 receiver -- Wired --> Headphone amplifier -- Wired --> Headphones
This configuration is somehow cumbersome (many cables are used and you have to sit close to the setup). For the record: there're devices combining a headphone amplifier with an AirPlay 2 receiver which slightly simplify the setup – they are usually more expensive because they carry other audio/connectivity features.
A simpler and more affordable solution would be to use Bluetooth headphones instead:
iPad -- Wireless --> AirPlay 2 receiver -- Wireless --> Bluetooth headphones
The WiiM Mini offers Bluetooth connectivity for wireless headphones. The Belkin SoundForm Connect doesn't offer Bluetooth connectivity. Basically, the WiiM can be used with the both scenarios I mentioned. The Belkin only with the first example.
