Customizing sections and subsections after \part{}

This is a follow up on an existing issue. (Originally posted by @weimiao1993 in https://github.com/josephwright/beamer/issues/615#issuecomment-669305043)

I wonder how I can customize sections and subsections after \part{}.

1. I found the bookmark for the subsection connection two lectures was misplaced. Besides, I got the warning `Package hyperref Warning: Difference (2) between bookmark levels is greater(hyperref) than one, level fixed on input line 62.'. Here is what I see from the PDF. The bookmark of subsection 2.2 in Lecture 2 is supposed to be at level 2. How should I fix it?
   

2. Can I display the name of the current section in the sidebar, while keeping the subsection numbering, after the command \part{}? Using the current code, the sidebar of Lecture 2 displays as subsec 2.2 \\ subsec 2.3 \\ Section 3 \\ subsec 3.1 . I would like some customization so that the sidebar of Lecture 2 becomes Section 2 \ subsec 2.2 \ subsec 2.3 \ Section 3 \ subsec 3.1.

Reproduce the reported PDF with \part{}, sections, and subsections; inspect the sidebar and hyperref bookmark output first. Compare the bookmark-level warning and the desired Lecture 2 sidebar layout, then determine whether the behavior is a bug or requires documented customization.