Add sponsored image P3A instrumentation for New Tab Page (uplift to 1.17.x)

[bsclifton]

Uplift of #6924
Resolves brave/brave-browser#12267

Approved, please ensure that before merging:

• You have checked CI and the builds, lint, and tests all pass or are not related to your PR.
• You have tested your change on Nightly.
• The PR milestones match the branch they are landing to.

After you merge:

• The associated issue milestone is set to the smallest version that the changes is landed on.

[bsclifton]

Tested on Nightly - put a detailed test plan in brave/brave-browser#12267

[kjozwiak]

test-browser failed on Linux as per https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-linux/2/execution/node/249/log. However, this is a known intermittent issue and will be fixed via brave/brave-browser#12351. Doesn't block uplift.

02:37:30  1 test failed:
02:37:30      AdBlockServiceTest.SubFrame (../../brave/browser/brave_shields/ad_block_service_browsertest.cc:527)

Restarting Win x64 via https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-windows/3/ due to build failing as per https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-windows/2/execution/node/85/log/.

[kjozwiak]

Restarting Win x64 via https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-windows/5/ as we ran into Agent was removed as per https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-windows/4/execution/node/189/log/.

16:20:04  Cannot contact i-00b3575ae47a19053-windows-swarm-dec75eeb: hudson.remoting.RequestAbortedException: java.nio.channels.ClosedChannelException
16:25:04  Could not connect to i-00b3575ae47a19053-windows-swarm-dec75eeb to send interrupt signal to process

Restarting macOS via https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-macos/4/ as test-unit and test-browser failed as per https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-macos/3/execution/node/234/log/ and https://ci.brave.com/job/pr-brave-browser-bsc-ntp-p3a-1.17.x-macos/3/execution/node/247/log/.

18:11:41  FAILED: obj/media/base/test_support/fake_demuxer_stream.o 

[kjozwiak]

Uplift into 1.17.x approved after deliberating with @brave/uplift-approvers. QA has verified the PR on Nightly as per #6924 (comment).