If you have a NAND backup from before launching CFW/homebrew, now would be the time to restore it because this will make your system clean enough to access the eShop. If not, you risk a ban by bringing the console online. Regardless of whether you have a NAND backup or not, updating your firmware will never affect your ability to use CFW/homebrew because the current exploit is hardware-based aka the software/firmware you are running doesn't matter. While the exploit is firmware-agnostic, CFW/homebrew are not and may need to be updated to the latest firmware which is usually why its not a good idea to update to the latest firmware. Right now, the best firmware is 7.0.1 but access to the eShop requires 8.X so you have to make a decision. Lastly, you don't "install" CFW on the Switch. The exploit is a temporary tethered coldboot that gives you CFW/homebrew until you turn off or restart the console. From the images you posted, I have no idea what CFW is on your SD card however I can link you the guides to setting up one of the currently available CFW.
ReiNX: https://reinx.guide/
Atmosphere via Kosmos: https://guide.sdsetup.com/
Atmosphere via Fusee: http://switchguide.xyz/
Huh, it looks like the install guides have changed a lot since then. I basically put the NX-bootkit master folder on my sdcard, ran the batch file, and Hekate would start. I never used this Tegra GUI. There is a folder for atmosphere on here, but I've never seen the Atmosphere startup before.
When you say "NAND backup from before launching CFW/homebrew" do you mean before launching for the very first time? I thought I backed up the NAND during the first time setting up but I can't find it anywhere so I'm backing it up now. But I'm probably just gonna start by following that Atmosphere via Fusee guide and start from scratch.
It sounds like I will need to find a way to update to 7.0.1. I saw a post above mention using nsps to update games and dlc.