Your best chance for recovery is through a professional disk recovery service. If the data can be retrieved, they are the ones to do it. Of course, these services are very expensive (don't be surprised by a four figure quote because the task is labor intensive,) but if the files are worth it to you, and you have the resources, consider it.
If you want to play around yourself, the first thing to do is purchase a hardware USB Write Blocker, perhaps something like this one if it works with your SSD, to make sure you don't accidentally or intentionally overwrite any of the data on your SSD as you start your explorations.
Next, check out The Sleuth Kit (TSK) and Autopsy. The Sleuth Kit is a free forensic analysis toolkit that includes disk analysis tools, including the ability to recover deleted files. Autopsy is a graphical front end to TSK and other tools, and includes modules to perform tasks like viewing images.
The trick to using Autopsy is to understand the language of its steps. Always keep in mind the tool is intended for use by law enforcement investigators, who are looking for evidence of criminal activity, such as child porn, drugs, lists of contacts, old emails, recently edited files, hacking tools, etc., and they speak their own language. None of that will apply to you, of course, but it helps to view the steps through their eyes.
Read the documentation, but the first thing you'll need is to create a case. That's just a file to track all the stuff you do. The case will then need a "data source" - all you do is pick "local drive", then your write-blocked SSD.
You then tell Autopsy to "ingest" the data source, which is where it runs a bunch of tools on the disk to figure out what's on it. Most of the law enforcement stuff won't apply to you, so when you ingest the data source, turn off the ingest modules for things that obviously won't apply, things like "hashes", "virtual machines", "email parsers", etc.
Autopsy will then start processing the disk. It runs in the background and can take a very long time; the larger the disk, the longer it takes. You can look at files as soon as it starts showing them to you, but once you confirm it's working, you may as well step back and let it finish.
You'll probably be most interested in using the manual tool called the Image Gallery Module. This is a fast viewer that will let you zip through all the images it finds. As you find files you want to save, you can right click on them and export them as local files.
Keep in mind that the tool is intended to find files that have been hidden or deleted. If you may have images on the drive (perhaps in your browser history) you wouldn't be willing to share with other members of your family, perform the drive recovery in private!
Good luck!
Apple appears to have discontinued the practice of making "delta" and "combo" updaters available on their support website starting with macOS 11 Big Sur, and so all updates after the OS X era are only available to download from the AppStore, Software Update System preference, and the command line utility.
If you have a second Mac with sufficient space to download and a USB drive that you are willing to erase, you might be able to create a bootable USB drive (or partition of one). Grab the installer either from the AppStore or the softwareupdate --fetch-full-installer 12.3
(use --list-full-installers
to find a different version), and follow the steps in this Apple Knowledge Base article: https://support.apple.com/en-us/HT201372
Possibly booting to Internet Recovery Mode might get you a full installer, but I'm not sure how it behaves with a nearly full disk. https://support.apple.com/en-us/HT204904 "On an Intel-based Mac, … you can use Option-Command-R during startup to be offered either the latest macOS that is compatible with your Mac"
Best Answer
This is an XY Problem
Formatting an external drive to APFS will not fix your issue.
You need to be able to connect to the internet - try wired ethernet instead of WiFi. As you blew away your internal drive completely, you have no source for Recovery except Internet Recovery or if you have access to another Mac on which you can make a bootable installer USB. There is no way to legitimately access a bootable installer from Windows.
Holding Cmd ⌘ R with no Recovery Partition should automatically switch to Internet Recovery instead. That it doesn't already hints at connectivity issues.
If all else fails, take it to an Apple Store - they will do it for you for free.