Spring AI MCP Server does not properly work when using spring.main.lazy-initialization=true

Bug description
I'm using spring-ai-starter-mcp-server-webmvc in my project to expose tools. I recognized that it gives me a 500 error when I set the property spring.main.lazy-initialization=false and I try to access the /sse endpoint.

Error

Caused by: jakarta.servlet.ServletException: java.lang.NullPointerException: Cannot invoke "io.modelcontextprotocol.spec.McpServerSession$Factory.create(io.modelcontextprotocol.spec.McpServerTransport)" because "this.sessionFactory" is null
	at org.springframework.web.servlet.function.ErrorHandlingServerResponse.handleError(ErrorHandlingServerResponse.java:70)
	at org.springframework.web.servlet.function.AbstractServerResponse.writeTo(AbstractServerResponse.java:105)
	at org.springframework.web.servlet.function.support.HandlerFunctionAdapter.handle(HandlerFunctionAdapter.java:112)
	at org.springframework.web.servlet.DispatcherServlet.doDispatch(DispatcherServlet.java:1089)
	at org.springframework.web.servlet.DispatcherServlet.doService(DispatcherServlet.java:979)
	at org.springframework.web.servlet.FrameworkServlet.processRequest(FrameworkServlet.java:1014)
	at org.springframework.web.servlet.FrameworkServlet.doGet(FrameworkServlet.java:903)
	at jakarta.servlet.http.HttpServlet.service(HttpServlet.java:564)
	at org.springframework.web.servlet.FrameworkServlet.service(FrameworkServlet.java:885)
	at jakarta.servlet.http.HttpServlet.service(HttpServlet.java:658)
	at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:195)
	at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:140)
	at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:51)
	at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:164)
	at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:140)
	at org.springframework.web.filter.CompositeFilter$VirtualFilterChain.doFilter(CompositeFilter.java:108)
	at org.springframework.security.web.FilterChainProxy.lambda$doFilterInternal$3(FilterChainProxy.java:231)
	at org.springframework.security.web.ObservationFilterChainDecorator$FilterObservation$SimpleFilterObservation.lambda$wrap$1(ObservationFilterChainDecorator.java:479)
	at org.springframework.security.web.ObservationFilterChainDecorator$AroundFilterObservation$SimpleAroundFilterObservation.lambda$wrap$1(ObservationFilterChainDecorator.java:340)
	at org.springframework.security.web.ObservationFilterChainDecorator.lambda$wrapSecured$0(ObservationFilterChainDecorator.java:82)
	at org.springframework.security.web.ObservationFilterChainDecorator$VirtualFilterChain.doFilter(ObservationFilterChainDecorator.java:128)
	at org.springframework.security.web.access.intercept.AuthorizationFilter.doFilter(AuthorizationFilter.java:101)
	at org.springframework.security.web.ObservationFilterChainDecorator$ObservationFilter.wrapFilter(ObservationFilterChainDecorator.java:240)
	at org.springframework.security.web.ObservationFilterChainDecorator$ObservationFilter.doFilter(ObservationFilterChainDecorator.java:227)
	at org.springframework.security.web.ObservationFilterChainDecorator$VirtualFilterChain.doFilter(ObservationFilterChainDecorator.java:137)
	at org.springframework.security.web.access.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:126)
	at org.springframework.security.web.access.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:120)
	at org.springframework.security.web.ObservationFilterChainDecorator$ObservationFilter.wrapFilter(ObservationFilterChainDecorator.java:240)
	at org.springframework.security.web.ObservationFilterChainDecorator$ObservationFilter.doFilter(ObservationFilterChainDecorator.java:227)
	at org.springframework.security.web.ObservationFilterChainDecorator$VirtualFilterChain.doFilter(ObservationFilterChainDecorator.java:137)
	at com.cumulocity.microservice.security.filter.PostAuthenticateServletFilter$1.run(PostAuthenticateServletFilter.java:44)
	... 94 common frames omitted
Caused by: java.lang.NullPointerException: Cannot invoke "io.modelcontextprotocol.spec.McpServerSession$Factory.create(io.modelcontextprotocol.spec.McpServerTransport)" because "this.sessionFactory" is null
	at io.modelcontextprotocol.server.transport.WebMvcSseServerTransportProvider.lambda$handleSseConnection$6(WebMvcSseServerTransportProvider.java:265)
	at org.springframework.web.servlet.function.SseServerResponse.writeToInternal(SseServerResponse.java:95)
	at org.springframework.web.servlet.function.AbstractServerResponse.writeTo(AbstractServerResponse.java:101)
	... 123 common frames omitted

Steps to reproduce

1. Clone the example repo: https://github.com/spring-projects/spring-ai-examples/tree/main/model-context-protocol/weather/starter-webmvc-server
2. Add spring.main.lazy-initialization=true to application.properties
3. Start the service
4. Try to access /sse endpoint

Expected behavior
The MCP server should be started and be accessible even when lazy Loading it set to true.

Minimal Complete Reproducible example
see above

Start with the starter-webmvc-server example linked in the reproduction steps and its application.properties, then inspect the WebMvcSseServerTransportProvider stack-trace entry. Reproduce the failure with lazy initialization enabled and verify that accessing /sse no longer produces the sessionFactory NullPointerException.