The Android versions of the Firefox and Yandex browsers have quite a few curious similarities like the lack of a traditional homepage in a tab as well as any way to set your own, not even by entering its address.
Nevertheless, by using our SwiftDial Launcher Extra-extension you can simulate having a traditional homepage even in those browsers.
Install the respective versions of SwiftDial and SwiftDial Launcher for your browser.
Navigate to some page in a tab and open SwiftDial Launcher from the browser menu's Addons section (if you tap the Addons menu button while on the browser home screen, it will open the Addons manager, which isn't needed for our purpose).
If you are using the SwiftDial YN variant, choose it in the Launcher settings.
Launcher adds an Open SwiftDial button on all websites you visit. You can choose the position, size, color and opacity of the button in the Launcher settings.
On browser startup, Launcher can open SwiftDial in a tab or replace the active tab with SwiftDial.
To do this, enable one of those options in the Launcher settings, then go to the browser settings.
On Firefox for Android set Homepage > Opening screen to Last Tab and Tabs > Close tabs to Never.
On Yandex Browser disable Start the app in a new tab and set Close tabs to Never.