Fixes ac for multiple publishers (uplift to 1.10.x)

[NejcZdovc]

Uplift of #5728
Resolves brave/brave-browser#10058

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[kjozwiak]

Looks like test-browser failed on Linux due to the following https://ci.brave.com/job/pr-brave-browser-multiple-publishers-ac-1.10/2/execution/node/417/log/

04:17:03  1 test failed:
04:17:03      BraveRewardsBrowserTest.CheckIfReconcileWasResetEmpty (../../brave/components/brave_rewards/browser/rewards_service_browsertest.cc:2941)

Above is a known issue and has been resolved via brave/brave-browser#10032. Doesn't block uplift.

@NejcZdovc @bsclifton looks like both test-unit and test-browser failed on macOS due to speedreader as per https://ci.brave.com/job/pr-brave-browser-multiple-publishers-ac-1.10/2/execution/node/528/log/ & https://ci.brave.com/job/pr-brave-browser-multiple-publishers-ac-1.10/2/execution/node/495/log/. Example:

04:39:53  FAILED: alwaysrununittests/test_install_name_speedreader 
04:39:53  python ../../build/gn_run_binary.py /usr/bin/install_name_tool -change @loader_path/../../Libraries/libspeedreader_ffi.dylib @executable_path/gen/speedreader/out/x86_64-apple-darwin/release/libspeedreader_ffi.dylib brave_unit_tests
04:39:53  error: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/install_name_tool: changing install names or rpaths can't be redone for: brave_unit_tests (for architecture x86_64) because larger updated load commands do not fit (the program must be relinked, and you may need to use -headerpad or -headerpad_max_install_names)
04:39:53  /usr/bin/install_name_tool failed with exit code 1
04:39:53  [3/6] STAMP obj/brave/components/speedreader/rust/ffi/test_install_name_speedreader_browser_tests.stamp

However, assuming this code doesn't touch any of the speedreader code. Is the above failure known?

[NejcZdovc]

@kjozwiak yup code doesn't touch speedreader, so completely unrelated

[kjozwiak]

Uplift into 1.10.x approved after deliberating with @brave/uplift-approvers. QA also verified the PR on Nightly as per #5728 (comment).