OK, so it's just a matter of the computer knowing the seed when I enter it manually?
Could I still sign on the hardware device?
You can still sign on the hardware device if you initiate a transaction from the hardware device, yes. But if you restore the seedphrase on the PC, then the signing is not going to happen on the device.
Or, if you go the "Use hardware device" route, then you would also be able to sign transactions from the device directly.
Hope this make sense.
I will only use Electrum on an airgap computer, so it makes no difference whether the seed stays on the device or I enter it manually on an airgap computer.
I would like to use the hardware wallet (Specter Shield), unfortunately it is not compatible with Electrum, but if I enter the Specter Shield seed manually into Electrum, I could still use the Specter Shield as a signing device, right?
There will be no connection between the device and Electrum in this case, because you're just restoring the seed. I'm not familiar with the device you mentioned, but I don't see how you would be signing from it.
It sound like you're trying to achieve something like this but using hardware wallets instead?
https://electrum.readthedocs.io/en/latest/coldstorage.html