I've created a simple starter - TimeStarter with RestController inside. Here is its pom:
<parent>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-starter-parent</artifactId>
<version>2.5.0</version>
<relativePath/>
</parent>
<groupId>ez</groupId>
<artifactId>time-starter-spring-boot-starter</artifactId>
<version>0.0.1</version>
<name>time-starter</name>
<properties>
<java.version>11</java.version>
</properties>
<dependencies>
<dependency>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-starter</artifactId>
</dependency>
<dependency>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-starter-web</artifactId>
<optional>true</optional>
</dependency>
<dependency>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-configuration-processor</artifactId>
<optional>true</optional>
</dependency>
</dependencies>
I've added TimeStarter to my project:
<dependencies>
<dependency>
<groupId>ez</groupId>
<artifactId>time-starter-spring-boot-starter</artifactId>
<version>0.0.1</version>
<scope>provided</scope>
</dependency>
<dependency>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-starter-test</artifactId>
<scope>test</scope>
</dependency>
</dependencies>
After that I expect that all necessary dependencies (spring-boot-starter-web) will appear in my project, and the REST controller from starter will be ready for HTTP requests. But no, I have to add spring-boot-starter-web and spring-web dependencies to make my starter work.
As M.Deinum said, the reason was I made my dependencies in starter "optional".