Apps showing OPEN in app store instead of download

If it says "Open" it means it still installed on the device. Which means it was not actually deleted.

The question then becomes, how exactly did you remove it?

If you selected move to App Library, or Remove from Home Screen it does not delete the app from the device.

You must select the actual "Delete App" option. If its not available, make sure Deleting Apps is set to Allow in Settings->Screen Time->Content & Privacy restrictions->iTunes & App Store purchases->Deleting Apps.

How exactly did you delete it? What steps did you follow?

If you went to Settings->General->iPhone Storage->App Name and selected the "Delete App" option it should have removed it completely from the iPhone.

If you did something else, please explain what that is.

You've tried closing the App Store app via the phone's taskbar and rebooting it ?