You have brought some weird assumptions that do not apply to my situation, and it has negatively impacted the quality of your advice.
(1) My iPhone broke. I do not have access to that iPhone anymore, as it fell into water and disabled the display. So all of the things you are telling me to do on iPhone are a complete non-starter.
(2) I do want to "use the same SIM on a non-iOS device." I want to take the SIM in my iPhone 6s, and use it in my non-iOS flip phone.
(3) The "SIM with the old number" is the only SIM that exists in this scenario. I took the sim card from my iPhone and put it in my Nokia flip phone. So my flip phone has the number my iPhone used to have. When people call the number that used to be associated with my iPhone, my flip phone rings, and I answer the phone, and we can talk. When people send texts to that same number, I do not receive any of those texts. It doesn't matter if they are iMessages or SMS or MMS, they do not appear on my flip phone.
(4) I was troubleshooting this problem with my provider, and they said the most likely reason my flip phone could not receive texts was that I had not deregistered iMessage. So I tried to do this.
(5) The link you included to deregister is the exact same link I went to. I did not have access to my iPhone (see point (1) if you are confused about this), so I used the second set of instructions, under the setting, "No longer have your iPhone?" which accurately described my situation.
(6) When I tried to follow the steps under "No longer have your iPhone?" the page attempted to send a confirmation code to me via text. This was an issue, because my phone does not receive texts, which is the whole reason I am trying to deregister iMessage, and my phone never received the text with the confirmation code. So I was unable to deregister iMessage because I couldn't receive the confirmation code that would have allowed me to complete the process.
(7) Thank you for including the GIF. However, only half of it is applicable to my situation. A more accurate GIF would involve you clicking "send code" in the screen on the right, and then a text message never, ever shows up in the screen on the left (which is not running iOS or Android but rather KaiOS 3.1).