Safari is an integral element of iOS/iPadOS - and cannot be updated independently of the OS. If your iPad has been updated to the most recent version supported by your iPad, then Safari is as up-to-date as is possible.
Many are reporting issues with accessing WhatsApp with the Safari browser after updating to iPadOS15.7.
Until (or indeed if) the WhatsApp portal is updated to accept connections from Safari, you’ll need to use another browser App. Firefox is reported to work well with WhatsApp:
https://apps.apple.com/gb/app/firefox-private-safe-browser/id989804926
As for Safari, some websites are known to incorrectly identify your iOS/iPadOS Safari User Agent when used in one or other of its browsing modes - of which there are two - these being Desktop and Mobile. Misidentification of the browser Agent can often manifest as the website reporting that your browser is out of date, or won’t properly render a page.
It’s easy to switch between modes if a website isn’t functioning correctly. From the desired web-page, touch the aA icon at the left of the Address Bar; this will reveal a menu. From the menu select Website Settings, then select (or deselect) Request Desktop Website, then tap Done. Now refresh the webpage.
The chosen setting will be saved for the selected website - and can be simply reversed if needed.