In a while I will be changing operator and SIM card, but not number. I backed up contacts, SMSs, even call logs. But I have no idea how to back up Whatsapp conversations. Do I need to worry? In other words, when I do such a change, do I risk losing my Whatsapp chats or are they linked to the number, implying they will get transmitted to the new SIM with the same number? Or perhaps they are linked to the device, which will also stay unchanged?
No. If you are keeping the number, then you need not worry about your Whatsapp account.
To backup conversations, go to whatsapp settings -> Chat and Calls -> Chat Backups. You can use Google Drive to backup to your Google account on Android devices.
Although you use your phone number as your account Id, the account is tied to device. You changing carrier has no effect on the account.