The Favourites Bar, if enabled, simply shows you your most recently saved Favourites - the full list for which, as you have discovered, is visible when you tap the “book” icon.
Let’s start by disabling the largely redundant Favourites Bar; you can always re-enable it later if you wish:
Settings > Safari > Favourites Bar - switch to OFF
Now, if you have a webpage that you wish to save, you can save it to your Favourites in several ways:
1) Touch-and-hold the “book” icon; when the Menu appears, touch Add Bookmark.
2) Tap the “share” icon (this being the little square with an upward-pointing arrow; from the menu, select Add Bookmark.
Both of these actions will save a “Favourite” to your Favourites list. With the list open (remember the “book” icon) just touch on any listed Favourite to open the corresponding webpage.
Similarly, if you open a new tab (this being the “+” icon, a page of icons will appear representing your saved Favourites; from here, you can simply touch an icon to open the link - or you can type something else entirely in the Address Bar.
Does this help clarify management of your Safari Favourites?
You might find the official iPad User Guide for iPadOS to be insightful. Here is link to both the downloadable version - and the corresponding online version:
https://support.apple.com/en-gb/guide/ipad/ipadf3dbb83f/ipados
I strongly recommend that you read the sections for the Apps that you use - as in doing so you’ll both understand and derive greater pleasure from using your iPad.
I hope this is helpful in resolving any difficulties and frustrations that you may have been experiencing.
