geotiff: extract writer entry points into _writers/ and reduce __init__.py to dispatch only (#1813 step 10) #1888

Reason

With the four read backends extracted (#1813 steps 7–9), __init__.py still holds to_geotiff (L1143), _write_single_tile (L1691), _write_vrt_tiled (L1757), write_geotiff_gpu (L3338), and write_vrt (L4417). Together that is about 1700 lines of writer logic. Splitting them mirrors the reader layout and reduces __init__.py to a thin dispatch file (about 150 lines: docstring, __all__, re-imports, open_geotiff body, deprecated plot_geotiff shim).

Proposal

Create _writers/eager.py (to_geotiff + private helpers), _writers/gpu.py (write_geotiff_gpu), _writers/vrt.py (write_vrt). Re-export the public names from __init__.py. The #1813 parity matrix uses to_geotiff as its fixture builder, so any writer regression breaks every parity cell, which is a strong backstop.

Drawbacks

Last and biggest writer-side change; reviewer needs to verify the writer bodies are unchanged except for imports. Mitigated by parity matrix and the existing writer test suite (test_features.py, test_compression*.py, test_writer_*.py).

Refs: #1813.