Chosen Solution
iPhone 7 Plus SIM tray will not eject using a SIM card eject tool or a paper clip. Applying a considerable amount of force does not produce any indication that the tray will eject. The tray is flush with the device and there is no bend to the device body. Paperclip can be inserted ~4x further into the SIM tray eject hole when compared to an iPhone 7 with functional SIM tray ejection. I see there is a SIM Eject Lever Replacement guide for the iPhone 6, but it is not clear to me if the same guide would be applicable for the iPhone 7 Plus.
To me it sounds like your iPhone 7 card spring is stuck in the eject position or broken. Broken doesn’t seem right to me, because those levers are metal. But to reset the card spring, you would need to open the device. Having the device opened and taking a picture of the sim card spring would help with this. Do you think you’re able to do that? Only reason is because card spring can’t be fixed from the outside, and getting a visual on the interior will allow us to know what may be the issue. Going to try and find a tutorial for you, because the 7 is pretty different from the 6. Update: Im trying to find a tutorial, but I can’t find one. Now that I think of it, there can be a few things wrong, but only one is your issue, but first let’s just see what the pictures look like from the top side of the board without removing the logic board. iPhone 7 disassembly guide: iPhone 7 Teardown Note: stop at the end of step 6 then take a picture