Set staging server preference after state is reset, not before (uplift to 1.12.x)

[emerick]

Uplift of #6221

[kjozwiak]

Looks like the Skip labels were added too late and all the plaforms ran either way. Going to mention the failures that happened below but won't be restarting as it's Android specific and that passed without any failures/issues.

Other failures (not blocking uplift nor restarting as per the above):

test-browser failed on macOS as per the following https://ci.brave.com/job/pr-brave-browser-rewards-fix-staging-switch-android_1.12.xx/1/execution/node/658/log/.

13:09:45  FAILED: alwaysrununittests/fix_test_install_name_brave 
13:09:45  python ../../build/gn_run_binary.py /usr/bin/install_name_tool -change @loader_path/../../Libraries/libadblock.dylib @executable_path/gen/adblock/out/x86_64-apple-darwin/release/libadblock.dylib -change @loader_path/../../Libraries/libchallenge_bypass_ristretto.dylib @executable_path/gen/challenge_bypass_ristretto/out/x86_64-apple-darwin/release/libchallenge_bypass_ristretto.dylib -change @loader_path/../../Libraries/libspeedreader_ffi.dylib @executable_path/gen/speedreader/out/x86_64-apple-darwin/release/libspeedreader_ffi.dylib brave_unit_tests
13:09:45  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)
13:09:45  /usr/bin/install_name_tool failed with exit code 1

Looks like Win x64 dropped the spot instance/agent removed as per https://ci.brave.com/job/pr-brave-browser-rewards-fix-staging-switch-android_1.12.xx/1/execution/node/221/log/.

12:16:12  Cannot contact i-04efdb04dd9d31b12: hudson.remoting.ChannelClosedException: Channel "hudson.remoting.Channel@7b426108:i-04efdb04dd9d31b12": Remote call on i-04efdb04dd9d31b12 failed. The channel is closing down or has closed down
12:21:12  Could not connect to i-04efdb04dd9d31b12 to send interrupt signal to process

[kjozwiak]

Uplift approved into 1.12.x after deliberating with @brave/uplift-approvers. QA has verified that enabling rewards staging is working on Nightly as per #6267 (comment).