macOS Sierra stuck in Recovery Mode and won't reinstall

Continued.....

I tried target recovery, but since my cable was not thunderbolt it didn't work. I don't have a thunderbolt cable and they are very expensive. Is there any other way? Otherwise I could ask a friend for a thunderbolt cable. Thank you for your help.

You can create a bootable macOS USB installer if you have access to another Mac model Late-2009 to mid-2022. The USB installer you can create depends on the exact model of the other Mac which must be compatible with macOS 10.13 High Sierra to macOS 12.x Monterey......the other Mac can currently be running any version of macOS.

Generally you need the following Mac models to install:

• • macOS Monterey -- 2015 to mid-2022
  • macOS Big Sur -- Late-2013 to mid-2021
  • macOS Catalina -- 2012 to mid-2020
  • macOS High Sierra -- Late-2009 to mid-2018

You can use the information in the following article to confirm macOS & hardware compatibility of the other Macs:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

You will need to follow the instructions in the Apple articles:

How to download and install macOS - Apple Support

Create a bootable installer for macOS - Apple Support

Make sure to use a good quality USB stick from a respected manufacturer (SanDisk are generally better) since the quality of many USB sticks are extremely poor and Macs are very picky about the drives used for booting.

I would recommend erasing the whole physical internal SSD of your 2016 laptop as GUID partition and APFS (top option). Unfortunately the physical drive is hidden by default in Disk Utility so with Disk Utility you need to click "View" and select "Show All Devices" before the physical drives appear on the left pane of Disk Utility. The physical internal Apple SSD should be the top most item called something like "Apple SSD AP256......".

If you do erase the internal SSD of your laptop, it will prevent you from accessing local recovery mode for Sierra that you have been using. You can wait & try to install macOS 10.13+ first using a USB installer, but if you still have issues with the instructions provided here, then you will need to erase the whole physical SSD since the partition or file system may be part of the problem. It is a risk, but you are basically at the end of the line anyway.

If after even erasing the whole physical internal SSD and using a properly created USB installer still does not work, then you may have a hardware issue of some sort. You can try taking the laptop to a local Apple expert to see if they can get macOS installed for you, but I wouldn't spend much money on this old laptop (for multiple reasons).