How Can I Check The Battery Health? (With Or Without 3rd Party Apps)

The battery health feature is exclusive to iOS for iPhone. Inclusion of this feature is relatively recent.

iOS/iPadOS for iPad has never had the Battery Health feature - most likely because iPad batteries are both considerably larger and have a much longer service life. 

An iPad battery is rated to maintain at least 80% of its initial capacity after 1000 full charge/discharge cycles - whereas an iPhone is rated to have 80% of initial capacity after 500 full cycles.

There are software packages available that can access battery cycle count. Popular choices for Mac are Coconut Battery and iMazing - whereas iMazing is available for Windows PC.

https://www.coconut-flavour.com/coconutbattery/

The iphone has a battery health option under settings, battery, the ipad doesn’t seem to. You can at least see what’s using the battery.

as to third party apps I have no suggestion, you’d just have to search and read reviews to find one that looks good to you