Persist NTP-SI index and for both Rewards and non-Rewards users

[tmancey]

New tab page sponsored image should be shown every 4th new tab (open, refresh, or relaunch of browser) and on the 2nd new tab (open, refresh or relaunch of the browser) for a fresh install. The index for when to show a new tab sponsored image should not change for non visible tabs during restoration of tabs.

[btlechowski]

Verification passed on

Brave	1.53.99 Chromium: 114.0.5735.133 (Official Build) beta (64-bit)
Revision	fbfa2ce68d01b2201d8c667c2e73f648a61c4f4a-refs/branch-heads/5735@{#1270}
OS	Ubuntu 18.04 LTS

Verified test plan from brave/brave-core#18433

Confirmed on fresh install the first NTT ad is shown on the 2nd new tab

Confirm subsequent NTT ads are shown every 4th new tab

Confirm browser relaunches persist the the count between new tabs

Confirm restored tabs (non visible) do not increment the count after relaunching the browser

Confirm opening a new tab and relaunching the browser many times shows an NTT ad every nth tab