Hello bro, iPads normally give 4.5 to 5 years good battery life. may be due to software level issue you may be experiencing battery drain. But if it was heavy usage for you in the past 2 years before applecare+ warranty ends you may consider replacing it.
Refurbished or serial number is only to identify whether its new device or got replaced at apple service center when we take it again in future to apple service center.
This is not a problem and you wont be seeing any performance difference. Its new device only. as the left over warranty will carry forward to your new replaced iPad Pro as well.
Replacement unit will again fresh start that 4+ years lifetime for normal users. So consider according to your usage and needs bor. because you will pay the replacement price service fee. if you find its worth go for it.