PERF: Index.join to maintain cached attributes in more cases

[lukemanley]

• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/v3.0.0.rst file if fixing a bug or adding a new feature.

import pandas as pd

data = [f"i-{i:05}" for i in range(100_000)]
dtype = "string[pyarrow_numpy]"

idx1 = pd.Index(data, dtype=dtype)
idx2 = pd.Index(data[1:], dtype=dtype)

# the is_unique call at the end is cached in this PR
%timeit idx1.join(idx2, how="outer").is_unique

# 59.1 ms ± 1.29 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)  -> main
# 41.9 ms ± 894 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)   -> PR

[mroeschke]

Thanks @lukemanley