Thanks! Just dove further into the matter…
I found that the current UEFN based on Unreal Editor 5.5 (v31.30) still bundles both the system and user installers with UEFN called VSCodeSetup-x64-1.78.1.exe and VSCodeUserSetup-x64-1.78.1.exe from April 2023. These files are typically located in C:\Program Files\Epic Games\Fortnite\VSCode\ or where you had the Epic Games Launcher install Fortnite to; along with two extension files themselves: Verse.vsix and URC.vsix.
I was on 1.77.3 because of an older MacBook while I like to keep versions in-sync, but upgraded slightly. I’m now on 1.78.2 and even consider your tip using the latest on this specific machine for UEFN.
After installing newer VS Code, I could use the Extension tab’s menu option “Install from VSIX…” and succeeded. Verse toolbar now appears and *.verse files are color-coded.
Thanks again @Mineblo and kind regards