It's almost like the computer needs the ability to run applications separate from the browser, to achieve tasks that are unrelated... What an idea that would be!
However some of the tasks you mention are very trivial. It seems hard to believe that you think a dedicated "app" is required for example your first example "convert a string to caps". This can be solved several ways on macOS out of the box.
TextEdit: New Document, (paste content), select all, Edit > Transformations > Make Upper Case
Terminal: pbpaste | tr 'a-z' 'A-Z' | pbcopy
Edit: oh and I forgot to mention, Preview.app (also built in) will open a gif as a series of image frames, so you can do as you wish with them.
- learn to use the command-line more, relying on documentation like http://cht.sh/magick, and http://cht.sh/python/uppercase
- learn to maintain graphical tools, like pqiv and AutoHotKey. I think this is the harder of the two
If I want to deal with pictures, I always use external programs, such as ImageMagick or my own Farbfeld Utilities (although Farbfeld Utilities cannot currently read animations, so ImageMagick must be used instead).
It is possible to download web pages to run them locally, if there is some function you want to do on a web page which is less shady. I don't know which web pages are designed to do that, but you can write some if you want to.
Honestly it sounds like a fun project idea: make a page that can do random little manipulations on text for you in JavaScript. But really you'd probably be better off just bringing up a terminal and running some imagemagick commands or echo "turn this into caps" | dd conv=ucase
But basically ChromeOs is what you describe...
Also observablehq.com is a collection of community-created javascript notebooks that run locally. You may be able to find all you need there...
myString.toUppercase()