Add system test coverage for partitioned-heat-conduction + fix issues #404, #674, #402#734

RajdeepKushwaha5 wants to merge 3 commits intoprecice:developprecice/tutorials:developfrom

RajdeepKushwaha5:gsoc2026/system-tests-improvementsRajdeepKushwaha5/tutorials:gsoc2026/system-tests-improvementsCopy head branch name to clipboard