CoW: Use weakref callbacks to track dead references
- [x] closes #55245
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

This is an alternative solution to #55518. What it happening here:

- Uses the `weakref.ref` callback to count the number of dead references present at the `referenced_blocks` list.
- Takes 20% more time at the constructor because of the function declaration!
  - The function declaration can be moved to the `add_reference` and `add_index_reference`, but this is just moving the performance hit to these methods.
- Everything is O(1) now, including `has_reference`. (`_clear_dead_references` is amortized to O(1))
- If the number of dead references is more than 256 and +50% of the array, it will prune these references
   - The implication is that the linear slow dead reference cleaning happens next to the GC calls, which I think this is a more intuitive behavior. 

(also check another possibilities at #55008)

Let me know if I should continue working on this solution.

Assuming this is an alternate solution to @phofl PR in #55518 #55518 needs to be back ported. This is something that we can consider for main and 2.2, but I want to test this more before we rely on it. I just fixed the tests. Any thoughts about it @phofl @WillAyd? Any news? Personally I would be more partial to exploring https://github.com/pandas-dev/pandas/issues/55631 (IMO I think the mental model of using a set would be simpler) Can you run the ``ctors.py`` benchmarks? Sorry for the delay. Here are the benchmarks:

| Change   | Before [593fa855] <main>   | After [98addada] <weakref-callback>   |   Ratio | Benchmark (Parameter)                                          |
|----------|----------------------------|---------------------------------------|---------|----------------------------------------------------------------|
| +        | 5.74±0.2ms                 | 7.37±0.2ms                            |    1.29 | frame_ctor.FromArrays.time_frame_from_arrays_int               |
| +        | 7.65±0.08ms                | 8.63±0.2ms                            |    1.13 | frame_ctor.FromArrays.time_frame_from_arrays_sparse            |
| +        | 1.43±0.07ms                | 1.47±0.06ms                           |    1.03 | frame_ctor.FromRecords.time_frame_from_records_generator(1000) |


 How does this correspond to the other timings in the issue? > How does this correspond to the other timings in the issue?

Not sure if I fully understand what is being asked, but this ~20% increase is from the overhead in the constructor. What this PR will be better is mainly at `has_reference`, which will be O(1) independently of the number of references. Insertions also should be a little faster because there is no periodic calls to the cleanings method, but this is probably not meaningful in any way, Updates? This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Hey @phofl, what is the current status of this PR? @phofl?  Hi, @phofl, can you give an update? Thanks for the PR but it does seem there much bandwidth or interest from the core team to pursue this approach so closing this out for now. Can reopen if there's renewed interest