I don’t think he went far enough. I don’t see that he added a final paragraph in the “be it resolved” section that failure to do these things would result in any penalty.
Since House and Senate are co-equal, he doesn’t have authority over them, but he does have authority to say what will and won’t be done on the issue in the Senate if House don’t do things fairly. On TV last night he did say the Senate wouldn’t act on anything, but that wasn’t included in his Resolution. (Did I miss it, or was he blowing sunshine up my skirt yesterday?)
He says many things, but usually they are conditional or qualified outcomes.
The Senate really doesn't have any power to correct a dysfunctional House, any more than the House has the power to correct a dysfunctional Senate - no matter how harmful to the institutions or the public the dysfunction becomes.
And as far as impeachment goes, the Senate has no role at all unless the House walks over articles of impeachment.
A that point the case is all "it depends" on the contents of the impeachment articles.
And nothing stops the Senate from conducting a sham trial either. Wouldn't be the first sham perpetrated by the government against the public.