The "Add to Home Screen" option hasn't gone anywhere. Its still in the Share menu.
You can tap the (...) icon at the bottom right of the screen, and then on Share and then scroll down the list to find the "Add to Home Screen" option.

What exactly do you mean by "clearing your browser"? The option to clear cache and website datasets is still in Safari's Settings in the Settings app ➜ Apps ➜ Safari.
The option to do so from the Bookmarks Menu / History also still there under the (...) icon.

If you mean something else, please clarify.
While you are in Safari's Settings you can return Safari to its previous layout style by selecting the "Top" layout in the Tabs section.

In the meantime, I would suggest the iOS 26 user guide.
click here ➜ Get started with Safari on iPhone - Apple Support