The "lower NEON bar" = new tab background image. The Deadpool guy in the theme I linked is new tab background image. The neon in my theme is new tab background image too. It's
new tab image because themes CAN'T modify any page outside of new tab page. You show the screenshot of
trendingpolitics.com and expect neon on that page, but no theme in the store can do such thing (only extensions can do this). What you need "doesn't work" in Chrome either. Both screenshots in Chrome Web Store show new tab page as you can see here (the address bar is empty):
https://chrome.google.com/webstore/detail/neon-kingdom-rnbow-neon-t/hcblhoelddfblfdajahoblegakkhlepl. There is no google logo because I use Clear New Tab. No one claimed there will be neon on all pages. The reason I linked that deadpool theme is to show that problem with missing neon (=new tab background image) is not unique to my theme. There's nothing I can do to fix this.
I will note in the description that neon appears only in new tab page (didn't realize it was confusing), but putting info about edge (or any other browser) will most likely count as "promotion of other browsers". It's Chrome Web Store after all.