Hi Yusuf,
Congrats on completing this project - it's definitely not an easy one!
The core CRUD (create, read, update, delete) functions work well, and I can see you have written all of your CSS from scratch, without relying on a component library which is a great way to really nail down the fundamentals of web development.
I can make some suggestions if you wish to fix some bugs in your solution:
URL structure
Currently, whenever a new board is selected, that boards name is used in the URL string. Whilst this is great for linking others to a particular board, the current implementation will return a 404 'Page not found' error, this is because the URL contains spaces.
The convention for URL strings is to use hyphens to separate words, along with all lowercase characters, e.g. /platform-launch. Since you are likely to be setting these URL strings programmatically, you could use some custom JavaScript code to handle this, although personally I would opt for using a package such as slugify
Touch targets
If we view the app on a mobile device, the board name is rendered as an h1 tag, with an img tag used to display the up/down caret, which handles the toggling of the board selection menu. Whilst this is possible to click with a mouse and some dexterity, it will be awkward to interact with on a touch device, especially for less able users. Furthermore, an img tag with an event handler like this does not convey any semantic meaning to users using assistive technologies such as a screen reader.
Instead, I would suggest using a button tag, with the caret img nested inside. This button element should have the event handler attached. You could also wrap the button in an h1 tag if you wish to preserve the heading styling and semantics.
<h1>
<button role='button' aria-haspopup='true'>
{board name}
<img src='caret.svg' aria-hidden='true' />
</button>
</h1>
Another element where you could apply similar logic would be the triple dots (ellipsis) that toggle the edit/delete board/task menus. These should be button elements with the svg img nested inside. Ideally you should also add some padding to the button element to make the clickable/touchable area larger.
Edit board
Removing columns from the board does not currently work, instead it simply just deletes the column name. The expected behaviour is for the entire column and all of its tasks to be removed from the board. Unfortunately since I am not familiar with Vue nor the structure of your application I cannot offer much advice here, but since this is a piece of core functionality in the application I recommend that you investigate this.
Once again, congratulations on completing this tough challenge!
Glen