The tags appended to your post suggest that you are using iPadOS 18 - this still being a beta release. In using beta software, you should have full expectation of encountering unexpected issues.
iPadOS 13 and later disables third-party cookies, by design, using ITP (Intelligent Tracking Protection) - this being a significant enhanced privacy feature of the OS.
First-party cookies can be still be easily enabled in settings:

If you known what you’re doing - and still wish to disable the privacy protection offered by ITP and third-party cookie blocking - you can do so from Safari Advanced settings.
Should you need to do so, the setting that you need to change works in reverse logic:
Settings > Safari > Advanced > Feature Flags > Disable Full 3rd-Party Cookie Blocking (ITP) - set to ON
The setting is shown here in its default (blocking) mode:
