eigen_tol in _spectral_embedding.py does not propagate to solvers other than arpack

Describe the bug

In _spectral_embedding.py the option

    eigen_tol : float, default=0.0
        Stopping criterion for eigendecomposition of the Laplacian matrix
        when ``eigen_solver='arpack'``.

does not appear to propagate to solvers ‘amg’ and ‘lobpcg’, e.g., adding eigen_tol and changing its value in examples/cluster/plot_coin_segmentation.py affects the outcome only if eigen_solver='arpack', which is the default but not for the other two: ‘lobpcg’ and ‘amg’.

Steps/Code to Reproduce

See above

Expected Results

eigen_tol works for all supported solvers

Actual Results

eigen_tol works for `eigen_solver=‘arpack’ only and is ignored otherwise

While at it

Also introduce and pass max_iter param to all eigen solvers, although maybe it should be named eigen_max_iter to avoid confusion.

Versions

System: python: 3.7.3 (v3.7.3:ef4ec6ed12, Mar 25 2019, 22:22:05) [MSC v.1916 64 bit (AMD64)] executable: C:\Users\Name\AppData\Local\Programs\Python\Python37\python.exe
machine: Windows-10-10.0.19041-SP0

Python dependencies: pip: 21.2.4 setuptools: 58.1.0 sklearn: 1.0 numpy: 1.21.2 scipy: 1.7.1 Cython: 0.29.24 pandas: 1.3.3 matplotlib: 3.4.3 joblib: 1.0.1 threadpoolctl: 2.2.0

[thomasjpfan]

To be backward compatible, we can have eigen_tol=None and pass in 0 to arpack, which is machine precision internally. For lobpcg and amg, we continue to pass in 1e-5 when eigen_tol=None. If eigen_tol is a float, we can pass it in directly.

Does this sound reasonable?

[lobpcg]

While at it, may be also fix https://github.com/scikit-learn/scikit-learn/issues/14713 ?