Solution
This can be done with spring-boot-starter-web:2.6.5 which makes use of spring-webmvc:5.3.17.
Add this config to your application.yml (or similar):
logging:
level:
_org.springframework.web.servlet.HandlerMapping.Mappings: debug
The underscore '_' in the logger name is important.
This property will generate logs during application boot that look like this

How it works
The property references spring-webmvc:5.3.17's org.springframework.web.servlet.handler.AbstractHandlerMapping which creates a hidden logger for mappings

This logger gets used in method detectHandlerMethods() of subclass AbstractHandlerMethodMapping

It looks like this technique goes back as early as spring-webmvc 5.3.5 (march 2021):
Github Spring Framework Release 5.3.5
Here's the commit containing the changes:
Github Spring Framework commit with changes for logging routes