There is NO SEARCH FIELD in iOS 13?

Search is still there - it just uses a gesture to which you are evidently unaccustomed.

From any home screen, from the centre of the screen (i.e., not the screen edges), just touch and swipe-downwards to reveal the Search box.

I strongly recommend that you read some of the early chapters within the iPad User Guide to iPadOS, downloadable for free within the Apple Bookstore App. Within the Bookstore App, just search for “Apple” to find all the comprehensive User Guides published by Apple.

I hope this both resolves you problem in finding Search - and provides a useful resource for learning all the new gestures and features of iPadOS/iOS.

If your swipe action is revealing notifications, then you are swiping-down from the top edge of the screen.

To repeat my earlier guidance - from any iPadOS home screen, from the centre of your physical touch-screen (i.e., NOT the screen edges), just touch and swipe-downwards to reveal the Search box.

This is the necessary swipe gesture, for iPadOS13.x, to summon the Search feature.

In reality, you can touch almost anywhere in the central area of the screen - just stay away from the edges!

I’m delighted that we got you there in the end.

I still strongly recommend that you download and assimilate the comprehensive iPad User Guide for iPadOS. It’ll answer many questions - and show you how to access the rich new feature set of iPadOS.