Alternatively (or in addition), we could also use this action or this one on pull requests to monitor the test coverage of all files changed.
A simple script could calculate the coverage of functions in the modified files:

1. Get all modified files

git diff --name-only $GITHUB_BASE_REF | grep -E '^[^(test)].*((\.h)|(\.cpph)|(\.cpp))$'

2. Get all corresponding tests TN: SF: <full/source/file/path> ... end_of_record ... from the trace file build/coverage.info
3. Get a list of all lines with functions in the corresponding file (All information should be contained in the trace file)

ctags -x --c-types=f <source/file/path> | grep function | awk '{print $3}'

4. Compute the coverage only for the changed files (SF: <full/source/file/path>) based on the trace file, e.g. function coverage using FNDA: <execution count>,<function>. (s. FILES section in lcov documentation)

Alternatively, it might be much simpler just to extract this information from the HTML coverage report using Beautiful Soup.