Depends on the platform, but generally speaking it requires taking whatever action changes its status from "unread" to "read." But even then, there has been at least one case of iOS malware that infected the system upon delivery of a text (since BlastDoor parsed the payload upon receipt, IIRC). That's one reason why Lockdown Mode rejects any text from unknown numbers.

How does one “open an email”

Same thing

Your messaging client may helpfully request the url they sent you to show a url preview.

In an email, your client renders the html including img tags (yes, this can be disabled, and may not even be default for most people anymore; it’s still a thing)

Text messages don't have an "open" action. Replying STOP will unsubscribe the recipient from future SMS from this number. I have never seen an organization use an unsubscribe as a positive action in their funnel. There are less expensive and less risky ways to confirm that a phone number is valid for sure.