• Open your Steam Profile in a Browser of your choice (Chrome will be used in here)
  
• Open the Element Inspector with F12 or right-click on your profile & select Inspect
  

Now this part is different.
Open a New Tab

• Go to the Profile Bundle who's Theme you're interested in &
  open a full Profile Bundle preview in a new window with the button right there:

Now on the standalone Bundle preview page;
• Open the Element Inspector with F12 or right-click here again like in the previous step;
  (we'll basically copy the Bundle preview's theme properties here)
  
• press Ctrl+F to open up a search box in the Element Inspector, something like this should pop up:
  

enter
• body.GameProfileTheme
  into the search & you'll find the theme properties:
  
  
  
• Now double-click the highlighted area
  & make sure that everything is selected with Crtl+A like this:
  

_______________________________________________________

Now switch to the Tab with your original Profile,

• find body.GameProfileTheme in the Element Inspector
  
• & replace your original Profile Theme properies with the ones you've copied from the Bundle preview.

I'll update the Guide when a simpler method is discorvered.

Below you'll find the old method to preview the legacy profile themes
(everything that got released before October 2022)

• Open your Steam Profile in a Browser of your choice (Chrome will be used in here)
  
• right-click on your profile & select Inspect
  

• scroll to the very top of the Elements Tab & there you will see your defined profile theme
  

• now double-click the highlighted area & replace it with the theme you want to preview

a list of all currently available themes can be found below!

• PinkTealTheme
  
• SummerTheme
  
• MidnightTheme
  
• SteelTheme
  
• CosmicTheme
  
• DarkModeTheme
  
• GhostTheme
  
• Winter2021Theme
  
• ColorNightmareTheme
  
• GreenSlimeTheme
  
• MutedRedTheme
  
• MutedBlueTheme
  
• MurugiahTheme
  
• BlueRedTheme
  
• FlatGreyTheme
  
• PurpleTheme
  
• SteamGreenTheme
  
• GoldBurgundyTheme
  
• BurntOrangeTheme
  
• GoldTheme
  
• VibrantBlueTheme
  
• Summer2021Theme
  
• GoldenProfileDebutTheme
  
• WinterProfile2020Theme
  
• GoldenWeekProfile2021Theme
  
• Lunar2022Theme
  
• SteamDeckTheme
  
• Steam3000Theme

Guess those will only get expanded in Steam specific events?
The method how new Game / publisher are applied has been changed.

+ their alternatives/duplicates
Profile Themes not listed here are either Default Themes or currently unavailable.