Corporate iPhone but on personal wifi. What can my employer see? Can they see my browser history and website?
Your company probably use an MDM (Mobile device management) on your phone.
From Apple website :

Not all settings and account information are exposed. You can manage corporate
accounts, settings, and information provisioned via MDM, but the user’s
personal accounts cannot be accessed.

Here are some examples of what an MDM can/cannot see :

Keep in mind that if a VPN is turned on, your company can see what you are doing on your phone.
Edit : I didn't see your comment. Google Device Policy can see the exact same things. Here is a detailed list.