I am currently using the Droid-ify client for F-Droid, and I can definitely update all my apps at once. I believe this "update all" option exists for the official F-Droid client (as well as other third-party clients), it might just be a colourful icon rather than text that you don't recognise.

I have it configured to install with Shizuku, if the default "session" installer doesn't work, it might be worth a try!

on the gui I have to first download the application and then click again to install it

What "gui"? Are you using the Google Play Store app or something? Because other apps like F-Droid, Obtainium, Aurora Store, or the default GrapheneOS App Store indeed do offer a one-click "update all" button. I cannot speak for Google Play, though.

I myself use Droid-ify and it has a setting for auto update. Note that, no auto update for third-party appstores below Android 13, including F-Droid.

In F-Droid, you can queue downloads up by clicking/touching every application you want to update, and IME it usually automatically installs the updates after downloading, too - but maybe that depends on settings, the specific version of F-Droid or the specific Android ROM you're running.