Reduce duplication in the failure handling methods for UKI/UTKI

Right now e.g. in UKI, we have to call different methods `update_ensemble_analysis!` and `succ_gauss_analysis!`.

https://github.com/CliMA/EnsembleKalmanProcesses.jl/blob/81e249a240a820da8b681300f881f33c4ac0160a/src/UnscentedKalmanInversion.jl#L607-L611

https://github.com/CliMA/EnsembleKalmanProcesses.jl/blob/81e249a240a820da8b681300f881f33c4ac0160a/src/UnscentedKalmanInversion.jl#L275

This is confusing, and at the very least, much of the logic is shared.

## Possible solution.

As these methods largely derive from calling `construct_mean` or `construct_successful_mean` (and the same with `cov`) , there should be a way of safely removing much of the code duplication outside of these methods,

Start in src/UnscentedKalmanInversion.jl at the cited update_ensemble_analysis! and succ_gauss_analysis! methods, then trace their construct_mean and construct_successful_mean calls and corresponding covariance logic. The refactor is done when UKI/UTKI failure handling shares the duplicated logic safely while preserving the existing successful and failure analysis behavior.

Written by the indexing model from the issue text.