No, SharePoint does not provide column-level security. But it is still possible to achieve your goal with a little creativity.
You didn't specify which version of SharePoint you are using, so I will give you a recommendation assuming SharePoint Online. If You post that you are using something different, I will adjust this accordingly.
You can lock the list down so that none of the managers have edit rights to your list at all.
Then create a dedicated user account specific for this purpose that does have edit access to the list.
Then create a PowerApp or use the new Flow UI to show them the item fields for approval, and put editable fields on the form only for the values you want them to submit. Create a custom connection for your Power App or Flow that logs in with the dedicated user account you created earlier. This app can then save the values the manager entered.
Another possible solution is by having two separate lists, one that is a "master" list with all the fields on it. The second list has a unique lookup column to the first, and a copy of the two fields you want editable.
A Flow configured for the "master" list ensures creating an item in the second list with the Lookup column pointing to the item that triggered the Flow, and potentially notifies the managers.
The managers can edit the fields in the second list, but have no contribute rights to the "master list". Then a Flow configured on the second list copies the values from those fields back to the master list whenever a change is made.