API and doc polish, some more deprecations to prepare for measures

[codecov[bot]]

Codecov Report

Patch coverage: 46.72% and project coverage change: +0.43 :tada:

Comparison is base (85ca926) 54.32% compared to head (6bbee4d) 54.76%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #414 +/- ## ========================================== + Coverage 54.32% 54.76% +0.43% ========================================== Files 116 116 Lines 5708 5608 -100 ========================================== - Hits 3101 3071 -30 + Misses 2607 2537 -70 ``` | [Impacted Files](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat) | Coverage Δ | | |---|---|---| | [ext/BATAdvancedHMCExt.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-ZXh0L0JBVEFkdmFuY2VkSE1DRXh0Lmps) | `100.00% <ø> (ø)` | | | [ext/BATUltraNestExt.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-ZXh0L0JBVFVsdHJhTmVzdEV4dC5qbA==) | `0.00% <0.00%> (ø)` | | | [src/algodefaults/default\_autocor\_len.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ29kZWZhdWx0cy9kZWZhdWx0X2F1dG9jb3JfbGVuLmps) | `100.00% <ø> (ø)` | | | [src/algodefaults/default\_eff\_sample\_size.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ29kZWZhdWx0cy9kZWZhdWx0X2VmZl9zYW1wbGVfc2l6ZS5qbA==) | `50.00% <ø> (ø)` | | | [src/algodefaults/default\_integration\_algorithm.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ29kZWZhdWx0cy9kZWZhdWx0X2ludGVncmF0aW9uX2FsZ29yaXRobS5qbA==) | `0.00% <0.00%> (ø)` | | | [src/algodefaults/default\_median\_estimator.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ29kZWZhdWx0cy9kZWZhdWx0X21lZGlhbl9lc3RpbWF0b3Iuamw=) | `0.00% <0.00%> (ø)` | | | [src/algodefaults/default\_transform\_algorithm.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ29kZWZhdWx0cy9kZWZhdWx0X3RyYW5zZm9ybV9hbGdvcml0aG0uamw=) | `41.17% <0.00%> (-12.67%)` | :arrow_down: | | [src/algotypes/bat\_default.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ290eXBlcy9iYXRfZGVmYXVsdC5qbA==) | `81.81% <0.00%> (ø)` | | | [src/algotypes/initval\_algorithm.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ290eXBlcy9pbml0dmFsX2FsZ29yaXRobS5qbA==) | `60.00% <0.00%> (+11.61%)` | :arrow_up: | | [src/algotypes/median\_estimator.jl](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat#diff-c3JjL2FsZ290eXBlcy9tZWRpYW5fZXN0aW1hdG9yLmps) | `0.00% <0.00%> (ø)` | | | ... and [45 more](https://app.codecov.io/gh/bat/BAT.jl/pull/414?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat) | | ... and [2 files with indirect coverage changes](https://app.codecov.io/gh/bat/BAT.jl/pull/414/indirect-changes?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=bat)

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