In Swift you can not have more than one active text-enabled question at a time, because each account is assigned only one phone number for response collection. When you activate a text-enabled question, it takes over the phone number to ensure that all the incoming responses are counted for the desired poll only.
That is not the case for web polls. All of the web enabled polls you create are always active. Every web-enabled poll has a unique URL, which you can find in the question's detailed view. Just click "Web voting" and you will be taken to the poll's unique URL.
Note: If you want your audience to join your web poll using an event code, they cannot access more than poll at a time. The poll that has been activated using the Start button will be visible.
Otherwise, you can provide the web polls' links to your audience, so that they access those directly.
Learn what is an event code.
Learn how to create web poll surveys.