Refactor Brave Ads file access - Follow up to 22340

[tmancey]

Description

See https://github.com/brave/internal/issues/877

Steps to Reproduce

• Fresh install
• Join Rewards
• Visit some websites
• Quit the browser
• Launch the browser

Actual result:

See https://github.com/brave/internal/issues/877

Expected result:

See https://github.com/brave/internal/issues/877

Reproduces how often:

Easily reproduced

Brave version (brave://version info)

Version/Channel Information:

• Can you reproduce this issue with the current release? Yes
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the nightly channel? Yes

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? N/A
• Does the issue resolve itself when disabling Brave Rewards? N/A
• Is the issue reproducible on the latest version of Chrome? N/A

Miscellaneous Information:

[btlechowski]

Verification passed on

Brave	1.42.65 Chromium: 103.0.5060.114 (Official Build) beta (64-bit)
Revision	a1c2360c5b02a6d4d6ab33796ad8a268a6128226-refs/branch-heads/5060@{#1124}
OS	Ubuntu 18.04 LTS

Verified in https://github.com/brave/internal/issues/877#issuecomment-1191166313