"Are these kinds of checks only against the number itself? Or is there some kind of dynamic registry?"
In general it is much simpler than that. These companies are sending you these SMS messages not from a "normal" phone number (xxx-yyy-zzzz) but from a shortcode (xxxxx). The "from" is a shortcode and only mobile numbers can receive SMS from shortcodes.
So if your number is not a "mobile" number, you might still receive SMS from other real phone numbers, but you cannot receive SMS from shortcodes.
Twilio, for instance, does not provide mobile numbers. Period. So even if you port a mobile number to twilio, as soon as it is theirs, you cannot receive SMS from shortcodes.
Your assertion that only mobile phones can receive SMS from shortcodes is not true in general, and additionally many verification SMS are not sent from shortcodes.
In general it is much simpler than that. These companies are sending you these SMS messages not from a "normal" phone number (xxx-yyy-zzzz) but from a shortcode (xxxxx). The "from" is a shortcode and only mobile numbers can receive SMS from shortcodes.
So if your number is not a "mobile" number, you might still receive SMS from other real phone numbers, but you cannot receive SMS from shortcodes.
Twilio, for instance, does not provide mobile numbers. Period. So even if you port a mobile number to twilio, as soon as it is theirs, you cannot receive SMS from shortcodes.