Is Sparrow Wallet trusted for such task?
It is good software for generating seed phrases, but it seems like you want to introduce more complexity than needed.
I'm planning on doing it on an offline PC without ethernet cable and booting Linux from a USB installation disk (Example:"Try Ubuntu before Install" option).
Just to clarify in case you didn't know about this: removing the ethernet cable alone does
NOT make the machine airgapped. You'll have to isolate it from
every network it can potentially connect. That means, removal of Wi-Fi and Bluetooth adapters at least.
Once the seed phrase is generated I'll backup and import it into an air-gapped hardware wallet.
My question is: why don't you generate the seed phrase on your hardware wallet? If you trust using it, then you should trust it for generating you the seed phrase.
Also, another question: which is the hardware wallet you own? The majority are not airgapped.