A nodejs 18 based Lambda importing from aws-sdk v3 fails to find the client-ssm package

I have writtena a Lambda function, based on NodeJS 18, that should send an openCypher query to a Neptune DB. The Neptune DB end point is stored as a paramater in the SSM. The below Lambda code fails with this error:

{
  "errorType": "Error",
  "errorMessage": "Cannot find package '@aws-sdk/client-ssm' imported from /var/task/index.mjs",
  "trace": [
    "Error [ERR_MODULE_NOT_FOUND]: Cannot find package '@aws-sdk/client-ssm' imported from /var/task/index.mjs",
    "    at new NodeError (node:internal/errors:393:5)",
    "    at packageResolve (node:internal/modules/esm/resolve:865:9)",
    "    at moduleResolve (node:internal/modules/esm/resolve:958:20)",
    "    at moduleResolveWithNodePath (node:internal/modules/esm/resolve:909:12)",
    "    at defaultResolve (node:internal/modules/esm/resolve:1173:79)",
    "    at nextResolve (node:internal/modules/esm/loader:163:28)",
    "    at ESMLoader.resolve (node:internal/modules/esm/loader:841:30)",
    "    at ESMLoader.getModuleJob (node:internal/modules/esm/loader:424:18)",
    "    at ModuleWrap.<anonymous> (node:internal/modules/esm/module_job:76:40)",
    "    at link (node:internal/modules/esm/module_job:75:36)"
  ]
}

I thought the aws-sdk v3 is already loaded for the Lambda with NodeJS 18. What am I missing?

The Lambda code:

import { SSMClient } from "@aws-sdk/client-ssm";
import { NeptuneClient } from "@aws-sdk/client-neptune";
import { GetParameterRequest } from "@aws-sdk/client-ssm/commands/GetParameterCommand";

const ssm = new SSMClient({
  region: "us-east-1",
});
const neptune = new NeptuneClient({
  region: "us-east-1",
});

export async function getParameter(parameterName) {
  const params = {
    Name: parameterName,
  };
  const request = new GetParameterRequest(params);
  const response = await ssm.send(request);
  return response.Parameter.Value;
}

export async function handler(event) {
  const NEPTUNE_ENDPOINT = await getParameter("simplify-mvp-dev-neptune-db-endpoint");
  const IAM_ROLE_ARN = await getParameter("simplify-mvp-dev-iam-role-secret-arn");

  const params = {
    DatabaseName: "db-simplify-mvp-dev",
    ResourceArn: IAM_ROLE_ARN,
    SecretArn: IAM_ROLE_ARN,
    Sql: `MATCH (n) RETURN n`,
  };

  const result = await neptune.runCypherQuery(params).promise();

  return {
    statusCode: 200,
    body: JSON.stringify(result),
  };
}