Ensure more specialised exceptions are raised in PyQGIS

[nyalldawson]

instead of the generic QgsException one
Refs warning in #55481 (comment)

/tmp/work/geography/qgis/work/qgis-3.28.13/build/python/core/build/_core/sip_corepart0.cpp:38168: warning: exception of type 'QgsProviderConnectionException' will be caught
38168 |             catch (QgsProviderConnectionException &sipExceptionRef)
      |
/tmp/work/geography/qgis/work/qgis-3.28.13/build/python/core/build/_core/sip_corepart0.cpp:38158: warning:    by earlier handler for 'QgsException'
38158 |             catch (QgsException &sipExceptionRef)

[github-actions]

🪟 Windows builds ready!

Windows builds of this PR are available for testing here. Debug symbols for this build are available here.

(Built from commit 51d7e9f)

[qgis-bot]

The backport to release-3_28 failed:

The process '/usr/bin/git' failed with exit code 1

stderr

error: could not apply 51d7e9ff1a1... Ensure more specialised exceptions are raised in PyQGIS
hint: After resolving the conflicts, mark them with
hint: "git add/rm <pathspec>", then run
hint: "git cherry-pick --continue".
hint: You can instead skip this commit with "git cherry-pick --skip".
hint: To abort and get back to the state before "git cherry-pick",
hint: run "git cherry-pick --abort".

stdout

Auto-merging python/core/qgsexception.sip
CONFLICT (content): Merge conflict in python/core/qgsexception.sip

To backport manually, run these commands in your terminal:

# Fetch latest updates from GitHub
git fetch
# Create a new working tree
git worktree add .worktrees/backport-release-3_28 release-3_28
# Navigate to the new working tree
cd .worktrees/backport-release-3_28
# Create a new branch
git switch --create backport-55576-to-release-3_28
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick 51d7e9ff1a1de84a4e6f6e9584c559338eb0dbfa
# Push it to GitHub
git push --set-upstream origin backport-55576-to-release-3_28
# Go back to the original working tree
cd ../..
# Delete the working tree
git worktree remove .worktrees/backport-release-3_28

Then, create a pull request where the base branch is release-3_28 and the compare/head branch is backport-55576-to-release-3_28.