You can do this by adjusting your Companies entity (table) slightly. Instead of having a field that is the users email you can use the out-of-the-box Owner field which comes with each entity. Using this field, you can then create a filtered view which has a condition to filter Companies where the Owner is equal to the current user. Similar to how the OOTB "My Accounts" view works.
Then in your Power App, you can set the filtered view as part of the datasource so that Companies are pre-filtered rather than doing the filtering in the app.