SSD FULL

As last restore and will require a really stable and reliable Internet Connection - best is Cable from Computer to Router over ethernet cable.

Restart computer and Immediately hold the 3 key combination Command + Option + r all together and at the sometime. This will be International's Recovery mode and will launch a connection to the Apple Servers. A Globe will load only as fast as the Apple Servers are running ant the speed of the connection form Router.

It will present options >> Disk Utilities >> View >> View ALL attached Drives. Choose the Upper Most Drive ( not the volumes indented and list below ). The drive normally is called Apple Media of Apple SSD - that is the drive to Erase and format as HFS Journaled with the GUID Partition Map. Once that is done >> backup out of Disk Utilities and choose install macOS. Follow the prompts and it may automatically reboot several time. Upon a final reboot - Setup Assist will present with the newer version of Mac X

@P.Phillips' instructions are how you need to proceed to erase the SSD. Those instructions erase the entire physical SSD so it does not matter if the SSD is full or not.

https://discussions.apple.com/thread/252908590?answerId=255468347022#255468347022

If you select "Show All Devices" within Disk Utility as suggested by @P.Phillips in the link you should see the top most item listed as "Apple SSD...." or something very similar. If you don't see this item, then most likely the SSD has failed and you will need to have the laptop repaired by Apple or an Apple Authorized Service Provider.

From the serial number provided (you should never post the serial number online) you have a MBPro 13" (2017) without touchbar. You should see if your laptop qualifies for this free Apple SSD repair program:

https://support.apple.com/13-inch-macbook-pro-solid-state-drive-service

Or this one for a free Battery repair program:

https://support.apple.com/13inch-macbookpro-battery-replacement

FYI, here is the current list of the publicly acknowledged free repair programs for various Apple products (some products like your laptop may have multiple programs):

https://support.apple.com/service-programs

It would help to have some more details.

What is the exact model of your Mac and its current OS? You can get this information by clicking the Apple menu and selecting "About This Mac" or by entering the serial number here:

https://checkcoverage.apple.com/

What OS are you trying to install?

How did you acquire the macOS installer or how are you booting to the macOS installer?

How much free storage space does the SSD have? You should always have at least 20GB of free storage space at all times for normal macOS operations. If you are trying to install macOS 11.x Big Sur you will need at least 36GB to 50GB of free space.

If you are trying to perform a clean install of macOS by first erasing the drive, then it should not matter whether the SSD is full. You just need to select the physical drive and erase it as GUID partition and MacOS Extended (Journaled) if you are installing macOS 10.11 to 10.13. The physical drive will be named something like "Apple SSD.....".

Make sure to have a good backup before you attempt to do anything.

If the drive is truly Full - one might have to Transfer files between two Mac computers using target disk mode

That or the attempt remove the OS and reinstall was done incorrectly. Thusly, portions of or All of the previous OS is still residing on the drive and occupying all the available space.

How to erase an Intel-based Mac

How to reinstall macOS

At this point - totally agree with @HWTech . Check if the machine qualifies for the SSD replacement and while at it the battery too. Should all be the cause of your issue and the parts are replaced at Apple expense - it will be like a new machine and get a few more years out of it.

You have attempted pretty much all possible form the comfort of Home / Office and now time to hand it off the Apple Authorized Repair Centre.

If time allows , do keep us posted on outcomes.