The following article describes two possible solutions when Access Request Settings are missing from Site Settings>Site Permissions.

Missing Outgoing Email Settings

When you navigate to the Site Settings > Site permissions and see the following view:

Verify Outgoing Email Settings in Central Administration:

Check out the following articles for possible configurations:

Inherited Permissions

(applies also to SharePoint Online)

The Access Request Setting is also missing when the site is inheriting permissions from its parent:

Stop inheriting permissions and the setting becomes available:

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