[Python] Improve Extension Types Support in PyArrow (umbrella issue)

### Describe the enhancement requested

This is an umbrella issue tracking open bugs and improvements related to extension types support in PyArrow.

**1. Extension types in nested arrays (struct/list):**
- https://github.com/apache/arrow/issues/34985
- https://github.com/apache/arrow/issues/37004

**2. Compute support:**
- https://github.com/apache/arrow/issues/22304
- https://github.com/apache/arrow/issues/33103

**3. Parquet/IPC (I/O) interoperability:**
- https://github.com/apache/arrow/issues/48254
- https://github.com/apache/arrow/issues/15068
- https://github.com/apache/arrow/issues/30080, related though closed as stale issues: https://github.com/apache/arrow/issues/30119 and https://github.com/apache/arrow/issues/22534

Stale but relevant:
- https://github.com/apache/arrow/issues/22572

**4. Pandas and other integrations:**
- https://github.com/apache/arrow/issues/33134
- https://github.com/apache/arrow/issues/49907
- https://github.com/apache/arrow/issues/32791

**5. Internal Python and API improvements:**
- https://github.com/apache/arrow/issues/39094
- https://github.com/apache/arrow/issues/24348

**6. FixedShapeTensor specifics:**
- https://github.com/apache/arrow/issues/35647

**7. Docs and warnings:**
- https://github.com/apache/arrow/issues/39007

If any additional cases related to extension types are not covered here, feel free to add them to the list.

### Component(s)

Python