Ipad pro takes a while to charge and dies very quickly, sometimes even gives me wrong percentage numbers

Those are almost identical symptoms I saw in my iPad 5 battery (2017) when it failed in 2021. Health was bouncing between mid-70s and the high 30s with about 850 cycles. Runtime from fully charged to shutdown averaged 13 minutes. Your battery is beyond help and requires replacement

The iPad repair page that LotusPilot links shows that Apple still performs battery service on 9.7-inch iPad Pros:

Based on my battery service experience for my iPad 5:

1) If available, use the "mail-in/ship-in" option to save a day on each end. Service does not happen in an Apple retail store but rather at a centralized refurbishment faculty.

2) Typically, Apple does not replace the battery in your device but rather ships you a fully refurbished device of identical specs but with a new battery and new outer shell.

3) Because of Item 2, you MUST make a full back-up of your old device before handing it over for service.

4) Apple will re-engrave a replacement device to match your old one, but that adds a few days to the process.

Using the ship-in option, I dropped my iPad a a USP Store on a Friday morning. Apple received it early Monday and I had a flawless refurb in hand before noon the following Wednesday. The replacement iPad has seen daily use since I received it on 2 January 2021.

It is your decision whether to repair or replace at this point.

Obtaining battery service for your 9.7" iPad Pro may be difficult - and being a device classified by Apple as "vintage", is perhaps unlikely to be a cost effective option:

Obtaining service for your Apple product after an expired warranty - Apple Support

You can check availability/eligibility for battery service - and associated cost for your country/region - here:

iPad Repair & Service - Apple Support

You might be well advised to consider replacing your aging iPad with a much newer model; even the current entry-level iPad10 will likely outperform your first generation iPad Pro.

The discharge curve of lithium ion batteries is not linear as it ages. Lithium ion batteries typically reach End of Life around 5 to 6 years after manufacture. As the battery ages, the curve becomes less linear and has a quick drop off of capacity. Your battery and what you’re stating, match the typical performance of an EOL lithium battery.

Given the age of your first generation iPad Pro 9.7", the battery is almost certainly at the end of its expected lifespan. If the iPad is in regular use, it is perhaps surprising that the battery hasn't already failed altogether.

You’re welcome! Now you’ve got to decide whether to replace the battery or upgrade or maybe both.