The SSDs in the MBPro 13" (2016 & 2017) non-touchbar model has an extremely high rate of failure.
OWC does sell a third party drop in replacement SSD for this laptop, but I don't recommend spending any money on this laptop for a number of reasons (Display & Keyboard issues are fairly well known, but there are other lesser known issues such as the USB-C ports wearing down so USB-C cables become loose causing intermittent connections--requires Logic Board replacement since the ports are integrated onto the Logic Board, plus the original factory battery had issues in this particular model). Unless you have recently had the Top Case/Keyboard Assembly or Battery replaced, then the battery is probably wearing out or failing (especially if it is the original battery from the factory).
As for using Internet Recovery Mode, you may want to try connecting the laptop directly to the router using an Ethernet cable for a faster more reliable network connection that bypasses difficult to troubleshoot WiFi issues.
In order to create a bootable macOS USB installer, you will need access to another working Mac compatible with macOS 10.13, 10.15, 11.x, or 12.x so you can follow Apple's instructions here:
Create a bootable installer for macOS - Apple Support
A compatible Mac for these operating systems is generally a model from Late-2009 to mid-2022 so that gives you a lot of choices to get an OS onto this laptop (I'm assuming you will be installing macOS to an external USB3 SSD since the internal SSD is bad).
Here are the general Mac models for each OS:
- macOS 12 2015 to mid-2022
- macOS 11 Late-2013 to mid-2021
- macOS 10.15 2012 to mid-2020
- macOS 10.13 Late-2009 to mid-2018
Here is an article which shows exactly which Apple hardware is compatible with various versions of macOS to confirm:
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
If you have never installed macOS 12.x Monterey on this laptop before, then you won't be able to do so now without a working internal Apple OEM SSD (even when you are installing macOS to an external drive ....it is a require only of the macOS 12.x Monterey installer because the Monterey installer will refuse to update the system firmware without a working properly formatted internal Apple OEM SSD installed).
FYI, you may still be able to boot to the internal SSD unless the SSD has failed completely. The usual problem with this SSD is that the SSD is slow to power on & go ready when starting or waking the laptop from sleep. If you Option Boot the laptop by holding the Option key immediately after hearing the startup chime, there is a chance this could give the SSD enough time to go ready & be seen on the Apple boot picker menu (aka Option Boot screen). If this works, then you may be able to use the "broken" laptop to download & create a bootable macOS 12.x USB installer.....just do not let the laptop go to sleep or the SSD will likely disappear again.
Actually I would highly recommend creating a bootable macOS 11.x Big Sur installer as well if Monterey had never been previously installed so if the internal SSD fails during the install of Monterey, then you have a backup option to install Big Sur.