Managing Mail application

Your iCloud email is saved automatically by iCloud and your device has a copy. In this way your mail is saved before you get to it. 

Because iCloud and your iPad synchronise with each other any changes you make on one will automatically be made on the other - and all of your devices signed into iCloud. This includes moving your iCloud mail into other mail boxes on your iPad, either manually or automatically. No doubt you already are moving mail into boxes to organise them in a way that suits you, but you can achieve this also by setting a rule or a series of rules to move or copy incoming mail to a specific mailbox, represented as folders on your device.

Unlike a Mac, you can’t set rules on an iPad to filter mail as it arrives, but you can set a rule in your iCloud account online. Sign in, go to Mail, select the gear icon at the top left of the screen, choose Preferences and then the last of the five options down the left side is Rules. 

Select Rules and then configure the options.

You can learn how to set rules in the support document Set up rules to filter email in Mail on iCloud.com

Note that these rules apply only to your iCloud email. If you have other services you will need to set rules for these separately, but in the same way - by signing into your account with a web browser.

I have my rules set on my Mac so I’m not overly experienced in using Rules from iCloud online. I’d be interested to see if this was of use to you on your iPad.