Globe projection rendering issues around the poles

Nobody has claimed this yet.

**mapbox-gl-js version**:

v2.9.1

**browser**:

Tested with the same outcome in latest versions of Google Chrome, Firefox and Safari.

### Steps to Trigger Behavior

Draw a polyline passing near the North Pole, use satellite map (I used the [bathymetry map](https://www.mapbox.com/blog/new-bathymetry-tileset-and-style-for-marine-maps)).

### Link to Demonstration

I can email a link if need be, not a public site.

### Bugs

1. Layers are not always fetched at a higher resolution on floating point zoom, such as when scrolling, causing the viewport to remain a low-res raster indefinitely (note vector layer is also rasterized), see 1.png. Resolves if I zoom in more.
2. Little white dots along tile boundaries (subtle, but highlighted with orange arc superimposed on the image under the dots), see 1.png. More glaring when panning.
3. Clipping causing large white triangles/polygons near the pole, see 2.png.
4. A red polyline near the pole shows as an enormous red polygon (interpolation to fill the gap near the pole also affecting layers on top of the base style?), see 2.png.

Start by reproducing the reported pole-crossing behavior using the stated v2.9.1 steps, the bathymetry map, and the attached images; no source file, test, or public demonstration is identified. Done means addressing the four reported symptoms: low-resolution tiles, tile-boundary dots, polar clipping, and the oversized polyline polygon.

Written by the indexing model from the issue text.