Incognito mode in Chrome is coded into the app. You can't remove it. There is no user option in Chrome's settings to disable it. As long as you don't invoke Incognito mode in Chrome you don't need to manage it. The only way to invoke it is intentionally, by tapping the ellipsis and tapping New Incognito Tab or from the Switch tabs page. To avoid it, create new tabs by tapping the plus sign to the right of the last tab while in regular mode. Close tabs by tapping the 'x' on a tab while in regular mode.
If the above is insufficient for your needs consider using Safari instead. You can disable Private Browsing in Settings. Navigate to Settings > Screen Time > Content & Privacy Restrictions and toggle on Content & Privacy Restrictions. From the same page navigate to Content Restrictions > Web Content and select Limit Adult Websites. If you aren't the only one using the iPad you may also want to set a Screen Time passcode. If so, make sure to set up Screen Time passcode recovery in the event you forget the passcode.