I am a little confused with some of your description. Tell me, please, where I am most confused. Looks like you are saying from your phone using the app, you are have problems connecting to the car. And your wife also is. That is one of the first signs of a failing eMMC.
Here's a link to one of our long threads on eMMC failures. 98 pages if you read all of it. But fortunately, the TMC admin folks have made this a Wiki and allows the first post to be updated many times. So please take a look. You might see other signs of eMMC failure you recognize on your car.
You said, "And the manual says it’ll also connect to my phone,.." Your cell phone will connect via Bluetooth to the car for making calls and listening to music streamed from Internet, phone to car. If you use a Hotspot or turn your cellphone's hotspot on, you should be able to connect your car via WiFi for an Internet connection. But Most of the older cars have free Premium Connectivity. Even those after 2018 or sold by Tesla as used cars after 2018, Tesla's $9.95 a month Premium Connectivity plan is a bargain. Unless you have firmware version 2021.32.xx, ever time that you 1) connect hotspot to car for Internet, then 2) put car in Drive, its going to disconnect from WiFi, even if Hotspot is still working. That's the way its been for 8+ years. Only recently have they changed that. Gotta have new firmware though.
You said, "but WiFi doesn’t see the phone,..." The car's connection to the phone will not be using the Phone's name. It you are using the phone as a hotspot, it will be by the name you use on your phone with you turn it on as a hotspot. Here's a hint that will save you some extra work. If you are going to use your phone as a hotspot, its a good idea to give it the name and use the password that you use at home for your WiFi SSID and password. That way, when you drive away from your home, the car will search for the same WiFi name.
I have never tried to use my phone as a hotspot and also connect the phone to the car's Bluetooth. I think it would work though.
Remember these simple rules. At home, you would want to connect the car to your home WiFi. And you want to connect your cell phone to your home WiFi, this might help you connect the cell phone > app > car better than away from your home WiFi. Maybe, can't guarantee it.
Please read that first post in that link. It will give you some insight from some really spare eMMC repair people.
Just so you know. Since 2018 when the first eMMCs started failing, there's been many failed. There's been hundreds of people ask thousands of questions with most of them asking the same thing just slightly different. Until Jan/Feb 2020, eMMC replacement was the only option. Hundreds or maybe thousands of us have bit the bullet and moved up to MCU2. I've seen only a few people that said they thought was was not worth it. I venture to say, 98% of us do/did and would do it again.
Did this help?
One more thing, how long should the upgrade take to complete? I dropped the car off at 9am this morning and I just got a message saying they are done. This morning they told me that the car would be there overnight till tomorrow afternoon because the garage was backed up. Did I just get lucky?
