Remove GitHub token build trigger warning (#1517)

docs/src/man/hosting.md

@@ -259,12 +259,6 @@ to the configuration file, as showed in the [previous section](@ref GitHub-Actio
     of the deployment is the same as the current repository. In order to push
     elsewhere you should instead use a SSH deploy key.
 
-!!! warning "GitHub Pages and GitHub Token"
-    Currently the GitHub Page build is not triggered when the GitHub provided
-    `GITHUB_TOKEN` is used for authentication. See
-    [issue #1177](https://github.com/JuliaDocs/Documenter.jl/issues/1177)
-    for more information.
-
 ### Authentication: SSH Deploy Keys
 
 It is also possible to authenticate using a SSH deploy key, just as described in

src/deployconfig.jl

@@ -414,17 +414,7 @@ function deploy_folder(cfg::GitHubActions;
     end
 end
 
-function authentication_method(::GitHubActions)
-    if env_nonempty("DOCUMENTER_KEY")
-        return SSH
-    else
-        @warn "Currently the GitHub Pages build is not triggered when " *
-              "using `GITHUB_TOKEN` for authentication. See issue #1177 " *
-              "(https://github.com/JuliaDocs/Documenter.jl/issues/1177) " *
-              "for more information."
-        return HTTPS
-    end
-end
+authentication_method(::GitHubActions) = env_nonempty("DOCUMENTER_KEY") ? SSH : HTTPS
 function authenticated_repo_url(cfg::GitHubActions)
     return "https://$(ENV["GITHUB_ACTOR"]):$(ENV["GITHUB_TOKEN"])@github.com/$(cfg.github_repository).git"
 end