Preface: I haven't used GrapheneOS personally, but I've learned as much as I can over the past year. I'll try my best.

If I installed these exact apps “sandboxed”, what exactly does that mean from a user standpoint? Will I have to use a separate account, reboot my phone, etc, or is it a quick process to use the app?

Sandboxed only means apps don't communicate with each other* and that if one got breached your entire system remains untouched, only the app gets affected. Installing and using apps is the same as normal Android, no extra steps involved. If you want, you can create a separate profile for "unsafe apps", but this is by no means a requirement and only ensures that if that profile gets breached the other profiles are untouched (profile sandboxing). Rebooting your phone is good practice after installing any software on any device, because some apps need a restart to complete the installation. It is not a requirement. To summarize: Just install the app, open it, and you're done. Apps are sandboxed by default.

Edit: The only thing you have to do before installing apps that rely on Google Play Services is to install Google Play Services in Settings (somewhere). This only has to be done once per profile.

*There are some exceptions, but for simplicity we'll stick with the textbook definition.

Is there a list of apps that I could browse to find equivalents to the above? Recommendations here are also ok.

AlternativeTo is a good place to find alternatives for certain apps.

I saw that Firefox isn’t exactly private(?) and that Vanadium is better in that aspect but I don’t understand why. Can someone ELI5, and help me see if this is a relevant concern for me?

This goes back to sandboxing. Basically, Firefox doesn't play nice with sandboxing. That means if Firefox gets hacked there is a greater risk of infecting the entire phone (which wouldn't happen with proper sandboxing). Vanadium has proper sandboxing, since Chromium (what Vanadium is based off of) was made for Android.

Think of Firefox as a metal crate with a few small holes poked in it. Those holes aren't a huge concern, since it would take a very skilled person to climb out of the crate through those small holes, but having holes in the first place is not great since it risks letting a person out of the crate. Chromium is a metal crate without holes, no risk of anyone getting out of that box, no worries.

Cheers!