New formatting API

[pitdicker]

This has now reached a basic working state that might pass the CI. Not that it ever did on first try...
There still is a lot to do when it comes to documentation and tests, and I should write down which attempts didn't work out.
But this is a start 😄.

Note that this PR relies on some preparatory work that is not all split out yet. The interesting commits start at "Add method to validate an Item can be formatted with an input type".

See #1127. cc @kamadorueda

[codecov]

Codecov Report

Attention: Patch coverage is 83.42541% with 120 lines in your changes are missing coverage. Please review.

Project coverage is 91.27%. Comparing base (0cfc405) to head (6e08273).

❗ Current head 6e08273 differs from pull request most recent head 45d7f15. Consider uploading reports for the commit 45d7f15 to get more accurate results

Files	Patch %	Lines
src/format/formatting.rs	77.58%	65 Missing ⚠️
src/naive/datetime/mod.rs	58.82%	21 Missing ⚠️
src/naive/time/mod.rs	71.62%	21 Missing ⚠️
src/datetime/mod.rs	91.78%	6 Missing ⚠️
src/date.rs	0.00%	4 Missing ⚠️
src/format/mod.rs	83.33%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1196      +/-   ##
==========================================
- Coverage   91.80%   91.27%   -0.53%     
==========================================
  Files          37       37              
  Lines       18148    18552     +404     
==========================================
+ Hits        16661    16934     +273     
- Misses       1487     1618     +131     

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