Copy paste from your first link:
In an interview with NBC News on Thursday, Osterholm clarified his comments, saying “it was not a recommendation. I have never made this recommendation to Biden’s group. We’ve never talked about it.”
“My only point was if we are going to keep making restrictions state-by-state, there is no compensation for the businesses that are being impacted,” he added. “What we’re doing right now is not working.”
Your second link does not include either Trump or Biden asking for a lockdown and is focused on local lockdowns and business closings that are happening in both Dem and Repub controlled states.
Biden's actual position:
https://www.bloomberg.com/news/articles/2020-11-15/biden-virus-advisers-say-a-national-lockdown-isn-t-on-the-agenda