Site Health Themes checkout isn't correct about automatic usage of default theme or themes condition in case of a broken theme

[oglekler]

1. In absence of a default theme Site Health says:

"Your site does not have any default theme. Default themes are used by WordPress automatically if anything is wrong with your chosen theme."

​https://yadi.sk/i/mP_59ss-3AsCCQ

It does not work this way:

1. PHP error in an active theme:

​https://yadi.sk/i/MuqOAQ0kjldWPw

2. Absence of an active theme:

​https://yadi.sk/i/Bzpy1icVk1Csiw

3. Absence of style.css — theme continues to work

And default theme is only activating automatically if you go to "Appearance > Themes" and formally something is wrong with theme, like an absence of style.css, but even if the theme can work fine but user after opening this page has no chouse what to do. It is not a convenient solution for a user not to see what was wrong and not to have a choice of what to do. More to the subject: #51479

2. Site Health don't tell about the absence of style.css which is causing the switch to default theme if you are visiting "Appearance > Themes". So, it does not run the same check what is doing this Themes page.

​https://yadi.sk/i/XeoY3c1x4rG_IA

[hellofromTonya]

Hello @oglekler and welcome to Trac. Thanks for this ticket.

Default theme logic existed before 5.6. Removing Version for now. Dropped into slack to double check.