Sure, here are some suggestions for improving the code:

1. Exception Handling: In the open method of the Page class, you are catching all exceptions and logging an error message. It would be better to catch specific exceptions that you expect might occur. This way, you can provide more specific error messages and handle different exceptions in different ways if necessary.

2. Code Duplication: There is a lot of repeated code in the Page class for fetching different types of elements (buttons, links, text boxes, etc.). You could create a private method that takes the CSS selector as a parameter and returns the elements. This would reduce the amount of duplicated code.

3. Logging: It's good that you're using logging, but it would be better to include more context in your log messages. For example, in the compare_elements method of the TestPage class, you could include the URL of the page where the elements were found.

4. Separation of Concerns: The TestPage class is doing a lot of different things: fetching elements, comparing elements, logging changes, writing updates, and taking screenshots. It might be better to split this class into several smaller classes, each with a single responsibility.

5. Magic Strings: There are several strings that are used multiple times throughout the code (like 'button', 'link', 'text_box', etc.). It would be better to define these as constants at the top of your file.

6. XPath Generation: The get_xpath method in the TestPage class seems to be a bit complex and might not work correctly for all cases. Consider using built-in methods from Selenium to generate the XPath.

Here's how you might implement some of these suggestions:

# Define constants for element types
BUTTON = 'button'
LINK = 'link'
TEXT_BOX = 'text_box'
# ... and so on for the other element types

class Page:
    # ...

    def _get_elements(self, css_selector):
        elements = self.driver.find_elements(By.CSS_SELECTOR, css_selector)
        for element in elements:
            element.descriptive_name = self.get_descriptive_name(element)
        return elements

    def get_buttons(self):
        return self._get_elements('button, input[type=button], input[type=submit], input[type=reset]')

    def get_links(self):
        return self._get_elements('a')

    # ... and so on for the other element types

class TestPage:
    # ...

    def fetch_elements(self):
        return {
            BUTTON: self.page.get_buttons(),
            LINK: self.page.get_links(),
            TEXT_BOX: self.page.get_text_boxes(),
            # ... and so on for the other element types
        }

    def compare_elements(self, elements, existing_elements):
        # ...
        logging.info(f'Element #{matching_elements[0]['Number']} {element_type} named {text} at {xpath} exists on page {self.page.url}')
        # ...

Remember, these are just suggestions. The best practices can vary depending on the specific requirements of your project.