Extract Common Logic to DBPUIDataBrokerProfileMatch for DBP UI Scan Results

[aataraxiaa]

Task/Issue URL: https://app.asana.com/0/72649045549333/1208507342220062/f

Description: This PR fixes an issue with Freemium PIR where the results displayed on the new tab page do not match the results displayed on the dashboard

Test Prerequisites

1. Set yourself as an internal user via Debug menu → Set Internal User State
2. Disable/Signout of Privacy Pro via Settings menu → PP → Remove from this device
3. Select Debug menu → Freemium -> Enroll into Experiment
4. Set the custom frontend UI URL via Debug menu → Personal Information Removal → Web UI → Set Custom URL. Enter https://abrown.duckduckgo.com/dbp
5. Use the custom frontend UI URL via Debug menu → Personal Information Removal → Web UI → Use Custom URL
   Relaunch the browser

Steps to test this PR:

1. Relaunch the browser
2. Open Freemium PIR via the banner on the new tab page
3. Enter profile data and perform a scan
4. Wait until it completes (or gets stuck 😅, a separate issue)
5. Note the scan results - the count of matches and broker sites (e.g 20 matches on 14 sites)
6. Relaunch the browser
7. You should see a banner on the new tab page and the results should match the previous results from the PIR dashboard

Definition of Done:

• Does this PR satisfy our Definition of Done?

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Internal references:

Pull Request Review Checklist
Software Engineering Expectations
Technical Design Template
Pull Request Documentation

[quanganhdo]

Tested and worked very well 👏 (the scan progress still gets stuck tho 🥲)