Move some configuration files out of the repository root (#64303)

This PR cleans up the repository root a bit, moving some of the less
relevant config files into the `.config` folder and removing unused
ones.

Release Notes:

- N/A

.github/workflows/deploy_docs.yml

@@ -109,7 +109,7 @@ jobs:
     - name: deploy_docs::lychee_link_check
       uses: lycheeverse/lychee-action@82202e5e9c2f4ef1a55a3d02563e1cb6041e5332
       with:
-        args: --no-progress --exclude '^http' './docs/src/**/*'
+        args: --config .config/lychee.toml --no-progress --exclude '^http' './docs/src/**/*'
         fail: true
         jobSummary: false
     - name: deploy_docs::install_mdbook
@@ -126,7 +126,7 @@ jobs:
     - name: deploy_docs::lychee_link_check
       uses: lycheeverse/lychee-action@82202e5e9c2f4ef1a55a3d02563e1cb6041e5332
       with:
-        args: --no-progress --exclude '^http' 'target/deploy/docs'
+        args: --config .config/lychee.toml --no-progress --exclude '^http' 'target/deploy/docs'
         fail: true
         jobSummary: false
     - name: deploy_docs::docs_deploy_steps::deploy_to_cf_pages