No way to select Standard post format in Formats filter

[SergeyBiryukov]

Background: #35497, #46591, #47359.

[45136] removed post format icons from the posts list table.

For some users, as noted in comment:52:ticket:35497, these icons were a convenient way to quickly distinguish posts with a format from standard posts.

Use case: when most of the posts have a non-standard format, you'd like check if there are any posts where you accidentally forgot to assign a format.

Even with the new Formats filter introduced in [44961], that's no longer possible, as it does not have a Standard option. This seems a bit inconsistent with the Categories filter, where you can filter by Uncategorized.

Brought up by @dimalash on support forums.

[sabernhardt]

The filter still does not have an option for Standard format.

(​forum post on the Russian how-to forum)

The Formats filter dropdown in the admin posts list table did not have a "Standard" option, so users could not filter for posts without an assigned post format. This was inconsistent with the Categories filter (which has an "Uncategorized" option) and removed a workflow that existed before the formats dropdown was introduced — distinguishing standard posts from formatted ones.

Added a "Standard" option that uses a NOT EXISTS tax_query to correctly find posts without a format.

Trac ticket:
https://core.trac.wordpress.org/ticket/47675

## Use of AI Tools

AI assistance: Yes
Tool(s): Opencode
Model(s): DeepSeek V4 Flash
Used for: Initial code skeleton; final implementation was edited and tested by me.