Question about Samsung Galaxy Watch

"Stand alone" means that the watch retains most of the important functions (calls, contacts, messages, etc.) even without a Bluetooth connection and basically works like a mobile phone with a SIM card. So you can leave your mobile phone at home and go jogging, for example, and you are fully reachable. When it is installed for the first time, an e-SIM is requested from the corresponding provider (provider login to their Internet portal is necessary for this) and then automatically stored on the watch and that's it.
Depending on whether your contract includes the option of an "additional device" (should be possible with all of them), this works without any problems and only has to be done once. Depending on your subscription, additional costs may be incurred (e.g. CHF 10 per month with SWISSCOM) or it is free of charge (SWISSCOM Infinty XL subscription).