However the electrum doc states
"New addresses are generated automatically when your receiving addresses are used"
How does this work then?
I suspect this is an error in translation from another language. As far as I know, Electrum does not automatically generate a new address every time a previous address receives bitcoins.
For instance I see forum sigs which include BTC addresses for donations or whatever. These people cannot possibly be changing their forum sig every time they receive a payment.
No, most of them don't. I prefer to use a new address for every transaction, so I don't put a donation address in my sig. Instead, if someone wants to make a donation to me, they must contact me and ask for an address.
How "temporary" are these addresses?
That decision is up to the user. You can continue to use an address for so long as you have access to the private key it you want. Keep in mind that any time you re-use an address you reduce anonymity and security.
And because of this, would the above scheme be better off using different wallets rather than different addresses within the wallets?
That depends on what you are trying to accomplish. When you send bitcoins from an Electrum wallet, you will not be able to choose which bitcoins are sent. The wallet will decide for you from among all the bitcoins in the entire wallet.
If a seedless wallet cannot send them, then what is the point?
It allows you to monitor your addresses and know when you've received bitcoins and how much bitcoins you have without having your private keys on a computer that is connected to the internet. That way if someone hacks into the computer or you end up with some malware running on the computer, your bitcoins can't be stolen. As long as you keep your seed you can always re-generate the wallet to send bitcoins from on another computer in the future.
What would be the best way to implement a scheme as the above?
Use wallets for the "accounts" I want? Use addresses for the "accounts" I want? Or something else?
That depends on what you're trying to accomplish.
I guess these addresses do not make sense as accounts, given that when sending I cannot choose from which address it is sent? So I would have to use different wallets to implement the above?
That depends on what you are trying to accomplish.