To turn off text notifications using the eBay app, open the eBay app and go to the Settings menu and select Notifications. From there, disable all options.
To disable most email notifications, you can use a desktop browser to go to your communication preferences and uncheck the options you do not want to receive.
https://commspreferences.ebay.com/commsprefs
That will allow you to disable many, but not all email notifications. To disable all email notifications, your best option may be to change the email address that eBay uses to send those notifications to an alternative email account, or else to filter eBay emails so they do not reach your email inbox.
