Can anyone provide a link to a handy step by step guide to "migrating your Electrum wallet to a new PC"?
You restore the wallet using the seed phrase. Basically that should be it.
What happens if I download Electrum onto my new laptop? Will my Bitcoin now be visible on both computers or do I make this one my "single wallet" as it were..?
Since the coins are not in the wallet, they're "on the blockchain" or "on the network" (overly simplified explanation), yes, both wallets should see (and work with) the same funds.
After you can see properly the funds on the new wallet, you can remove the old one if you want to. Or not. As you prefer.
I will add that Electrum on Windows is just as safe as your Windows system (so malware is a real threat). So if you have meaningful funds in your wallet you may consider getting a hardware wallet and move your funds there.
Also, with the wallet on 2 PCs, there are 2 places that can get malware/hack (also you have to be overly careful if you ever want to sell/give away the older PC, some people do know how to recover even removed wallets).
So another worthy "path" could also be to make a new wallet on the new PC and send the funds there (but, again, I prefer the path of hardware wallet, which in my case can be used with Electrum).