Inconsistent handling of custom extensions in the generated OpenAPI documentation

[MateuszPe]

Describe the bug
There is inconsistent handling of custom extensions in the generated OpenAPI documentation when using springdoc-openapi. Specifically, custom extension properties without the x- prefix are not added to the OpenAPI definition in recent versions.
It seems that this breaking change was not described in the release notes, causing unexpected behavior for users upgrading from earlier versions.

To Reproduce
Generate openapi for a controller with a defined custom extension.

@RestController
@RequestMapping("/hello")
class HelloWorldController {

  @Operation(
      summary = "Hello World",
      description = "Returns a simple Hello World message",
      extensions = {
          @Extension(
              properties = {
                  @ExtensionProperty(name = "custom-extension", value = "custom-extension-value")
              }
          )
      }
  )
  @GetMapping
  public String helloWorld() {
    return "Hello World";
  }
}

To generate openapi below test can be used:

@SpringBootTest
@AutoConfigureMockMvc
class OpenapiGenerationTest {

  @Autowired
  private MockMvc mockMvc;

  @Test
  void shouldGenerateOpenapi() throws Exception {
    MvcResult result = mockMvc.perform(get("/v3/api-docs"))
        .andDo(print())
        .andExpect(MockMvcResultMatchers.status().isOk())
        .andExpect(MockMvcResultMatchers.content().contentType("application/json"))
        .andReturn();

    Path filePath = Paths.get("openapi-docs.json");
    Files.write(filePath, result.getResponse().getContentAsString().getBytes());
  }
}

• What version of spring-boot you are using?
  3.4.2

• What modules and versions of springdoc-openapi are you using?
  springdoc-openapi-starter-webmvc-api v2.8.4
springdoc-openapi-starter-common v2.8.4

• What is the actual and the expected result using OpenAPI Description (yml or json)?
  Library does not add custom exception to openapi definition.
  Generated openapi specification must have defined by annotations extension.

• Provide with a sample code (HelloController) or Test that reproduces the problem

@RestController
@RequestMapping("/hello")
class HelloWorldController {

  @Operation(
      summary = "Hello World",
      description = "Returns a simple Hello World message",
      extensions = {
          @Extension(
              properties = {
                  @ExtensionProperty(name = "custom-extension", value = "custom-extension-value")
              }
          )
      }
  )
  @GetMapping
  public String helloWorld() {
    return "Hello World";
  }
}

Expected behavior
Generated openapi must have extension in definition.

Additional context
2.6.0 - this version generates extension property "as it is". Name of the extension is exactly the same as defined by user.
2.7.0 - this version generates extension property with x- if extension property name is not prefixed with x-. It it is prefixed then generated definition contains extension property.
2.8.0 - this version generates extension property ONLY when it was defined whit prefix x-. Otherwise extension property is not present in openapi definition.

[bnasslahsen]

@MateuszPe,

2.8.x is based on OAS 3.1: Refer to https://swagger.io/specification/
This object MAY be extended with Specification Extensions, though as noted, additional properties MAY omit the x- prefix within this object.

You can still use old behavior by switching to OAS 3.0:

springdoc.api-docs.version= openapi_3_0