Block toolbar and classic block header awkwardly obscures Notices

[MadtownLems]

Description

The Classic Editor block obscures notices.

Step-by-step reproduction instructions

Create a post with a Classic Editor block at the beginning, and enough filler text below it to allow scrolling.
Publish it.
Type some random changes in the post, let it idle long enough to generate an auto save, then leave the page. (This step is just to get a notice displayed on the page when we reload it.)
Edit the post. You should now have a notice about the Autosave.
Scroll down so that the notice overlays the Classic Editor block.

Expected behaviour

The Notice div should remain on top, with my content going behind it.

Actual behaviour

The Classic Editor box that says "Classic" shows up in FRONT of the notice, even though the content of the classic block goes behind it.

Screenshots or screen recording (optional)

Attached

WordPress information

• WordPress version: 5.7.3
• Gutenberg version: whatever comes with 5.7.3
• Are all plugins except Gutenberg deactivated? yes
• Are you using a default theme (e.g. Twenty Twenty-One)? yes

Device information

• Device: Desktop
• Operating system: Windows 10
• Browser: Chrome: 90.4

[MadtownLems]

I've noticed that this extends beyond just obscuring Notices. The "Classic" box sits in front of other

block controls as well. See attached screenshot.

[talldan]

The block toolbar also overlaps notices:

[paaljoachim]

I noticed the same bug. I added this issue: #32115 (Which I will now close as a duplicate.)

[jasmussen]

I have a solution, if not a fix, in #32238.