I can't update the app store, it asks for another Apple ID

Deleting the AppStore on your iPhone will not help, if a different Apple ID is shown for apps you want to use or update.

Go to Settings/Your Name/AppleID/Media & Purchases and log out of the account. Then log in again with the Apple ID you are using on this device.

You are trying to update (Aktualisieren) the Apple Store app, and you seem to have used a different Apple ID Mail address for the download before.

Delete the Apple Store app on your iPhone and download it again from the AppStore on your iPhone.

If you have apps on your iPhone, that have been downloaded using a different Apple ID, delete them and download them again, this time using your Apple ID.

Has the iPhone been set up with your Apple ID?

If an app that you want to update shows a different Apple ID, you will have to delete the app and download it again.

Has the iPhone been set up with your Apple ID when you bought it, or did it have a previous user, and there are still some apps installed from that user?

In the support article: If you subscribe to Apple One and use a different Apple ID for iCloud - Apple Support Apple alludes to using a different Apple ID for media, subscriptions, and purchases, but doesn't describe how to do this.

In iOS/iPadOS: Go to Settings > [your Apple ID] > Media & Purchases. Sign out of the current ID and sign in with a different one.

In Ventura: First, quit Settings. Then, in App Store, choose “Sign Out” in the Store menu, then click on the “sign in” button that appears in the main window. You can then sign into the other account. (from: Using different Apple ID for media & … - Apple Community )

The Author wanted to update the Apple Store App on his phone.

He posted a link to a shared video, which clearly showed the Apple Store App, and not the AppStore. But the link was deleted by the moderators.

Ingo2711 wrote:

Delete the Apple Store app on your iPhone and download it again from the AppStore on your iPhone.

Actually you cannot delete the App Store app. --> Delete built-in Apple apps from your iPhone, iPad, or Apple Watch - Apple Support

Okay, I didn't see any image. All I was seeing was the author asking: "Can I delete appstore ???" and "I can't update the app store"

Plus so many people use the terms App Store and Apple Store synonymously (Apple is really bad about not giving things clear and distinct names)