Run a tighter ship: Additional pre-commit checks and CI

[drbenvincent]

• protect main
• add tests to pre-commit checks?
• check notebooks cell execution order in pre-commit checks
• add spelling to pre-commit checks. See https://github.com/Anadea/pre-commit-config-shellcheck
• add local doc build to pre-commit checks?
• set up CI for remote checks to protect main?