Depends on your local laws and such, but in most European countries you can get a prepaid SIM card for a couple of euros/pounds/whatever at any supermarket, making them practically free. If you need a temporary number for a scammy special offer or any situation where your number is publicly visible (Gumtree, etc) it’s a no-brainer IMHO.
If your phone suppprts running two SIMs at once, it has two IMEIs so as far as the network(s) are concerned it’s two distinct handsets unless they deduce otherwise.
A fun aside: years ago I did some work for a small phone company (the company was small, not the phone) and they gave me a SIM with 100 numbers in a block and access to a portal I could manage them with. Sadly, I forgot to pay the annual £10 renewal fee.
I’m stealing that line, thankyou.