build: Add support for Python 3.10 across all backends

[matthewfeickert]

Description

Follow up PR to PR #1808

• Add support for Python 3.10 to the PyPI metadata and codemeta.json.
• Update Dockerfile base image to python:3.10-slim-bullseye.

Checklist Before Requesting Reviewer

• Tests are passing
• "WIP" removed from the title of the pull request
• Selected an Assignee for the PR to be responsible for the log summary

Before Merging

For the PR Assignees:

• Summarize commit messages into a comprehensive review of the PR

* Add support for Python 3.10 to the PyPI metadata and codemeta.json.
* Update Dockerfile base image to python:3.10-slim-bullseye.

[codecov]

Codecov Report

Merging #1809 (d93e4e4) into master (05e1338) will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##           master    #1809   +/-   ##
=======================================
  Coverage   98.14%   98.14%           
=======================================
  Files          64       64           
  Lines        4270     4270           
  Branches      719      719           
=======================================
  Hits         4191     4191           
  Misses         46       46           
  Partials       33       33           

Flag	Coverage Δ
contrib	26.25% <ø> (ø)
doctest	60.60% <ø> (ø)
unittests	96.13% <ø> (ø)

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