CP algs: Move main tests to CA

Move main CP algorithms tests to CA. This is draft for now due to the following caveats

• will eventually re-target to 24.0 once the CI will be green here to properly test for the analysis
• taus SFs differ for sequences

Note this is just part one that will also go to 24.0 to avoid having integration tests running legacy configuration.

/cc @krumnack @gwatts @ekourlit @jcatmore @jchapman @nstyles