[Site Logo] Previous theme's site_logo renders instead of current custom_logo (when switching themes)

Description

This issue was originally reported in WordPress Core Trac https://core.trac.wordpress.org/ticket/53817.

An edge case was identified in Trac 53770 where when a previous theme's logo renders when switching back to a theme.

WordPress 5.8 introduced new functionality (in _override_custom_logo_theme_mod()) where, when exists, the 'site_logo' option is used instead of the theme's 'custom_logo' mod. See Trac 53247 / r51091.

What happens when switching back to a theme that has a custom logo stored in its theme mod option? It no longer renders that theme's custom logo but instead renders what's stored in the 'site_logo' option. The 'site_logo' was set by the previous theme.

This is a breaking change from 5.7.2 and earlier.

Is this the expected behavior?
Should the site logo be the logo regardless of the theme?
Does it provide a better experience for site owners by maintaining consistency when switching between themes?

In other words, is this an edge case that needs to be fixed OR is this new behavior by design?

Step-by-step reproduction instructions

Go to Appearance > Themes > Activate the Twenty Twenty-One theme.
Go to Customize > Site Identity > Select logo (under Logo setting) and set the logo.
Click Publish.
Exit Customizer.
Go Themes > Activate the Twenty Twenty theme.
Go to Customize > Site Identify > Select logo but select a different logo this time.
Click Publish.
Exist Customizer.
Go back and active the Twenty Twenty-One theme again.
Go back to Customize > Site Identity.

Notice:

The logo is the one set in Step 6 (for the Twenty Twenty theme) and not the one set Step 2 (for TT1).
The IDs are also different in the options database. For example:
- theme_mods_twentytwentyone "custom_logo";i:52;
- theme_mods_twentytwenty "custom_logo";i:47;
- site_logo = 47

Screenshots, screen recording, code snippet

WordPress 5.7.2: TT1 has a white logo and TT has a black logo 53817-5 7 2

In WP 5.7.2. as shown in the gif:

The logo stays bound to its theme
Switching to a theme without a logo shows no logo
Switching to back to a theme that had a logo set shows its logo and not the previous theme's logo

WordPress 5.8.0: TT1 should have a white logo and TT should have a black logo 53817-5 8 0

In WP 5.8.0 as shown in gif:

Switching to a theme without a logo shows the logo set from the previous theme
Switching back to a theme that had a logo set does not show its logo but rather the logo from the previous theme

Environment info

No response

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WordPress / gutenberg