Figure.clip_xxx: A consistent API for clipping by polygon, land, water, solar, and mask

GMT supports several related clipping operations:

Description | Activate | Deactivate | User input
-- | -- | -- | --
Clip land areas | `coast -G` | `coast -Q` | No
Clip water areas | `coast -S` | `coast -Q` | No
Clip by polygon | `clip` | `clip -C` | (x, y) coordinates
Clip by mask | `mask` | `mask -C` | (x, y) coordinates
Clip by a country or region code | `coast -E+c` | `coast -Q` | No
Clip by solar terminators | `solar -G` | `clip -C` | No

For every mode, subsequent plotting commands are clipped until the path is explicitly ended. This stateful behavior makes clipping a natural fit for context managers.

**Possible API designs:**

1. Low-level begin/end methods
```
fig.begin_clip(data=polygon)
fig.plot(...)
fig.end_clip()
```
This closely mirrors GMT, but requires users to end clipping explicitly and can leave a clip path active after an exception.

2. A single context-manager method with a mode
```
with fig.clip(mode="polygon", data=polygon):
...
with fig.clip(mode="land"):
...
with fig.clip(mode="dcw", code="US"):
...
```
This has a compact API, but each mode wraps a different GMT module and accepts different parameters. Documenting and validating this mixed argument set could become complicated.

3. A `clip` namespace
```
with fig.clip.polygon(data=polygon):
...

with fig.clip.land():
...
```
This groups related functionality neatly, but may be challenging to expose and document correctly. See the proof of concept in #3878.

4. Explicit context-manager methods
```
with fig.clip_polygon(data=polygon):
...
with fig.clip_land():
...
with fig.clip_water():
...
```
This one is much easier to document that option 4. A POC PR is at #4703.

I feel option 4 is the best API design.

Start by reviewing the proof of concept in #3878 and POC PR #4703, then compare the four API designs against the listed GMT clipping modes. Done means the project settles on an API and defines coverage for polygon, land, water, mask, DCW, and solar clipping.

Written by the indexing model from the issue text.