Older iPad models cannot be updated to newer iPadOS versions, correct.
Apps require specific ios or iPadOS versions, as well.
Wi-Fi works for iOS and iPadOS updates, and works for app updates.
You have the central limit here backwards, though. Wi-Fi can update all. Use of cellular (SIM or eSIM) can block larger updates, as iOS and iPadOS updates and larger-app updates are not available via cellular prior to 5G cellular and a 5G cellular plan. Tomuse cellular, you’ll need a 5G plan, 5G coverage, 5G iPad, and a sufficiently data cap for updates vis cellular. Otherwise, Wi-Fi is needed for iOS or iPadOS updates, and for larger-app updates.
Which iPad, and which iOS or iPadOS version?
How to: Identify your iPad model - Apple Support
Version: Settings > General > About