When I add this BucketDeployment to my CDK CodePipeline, cdk synth never finishes

I'm trying to use CDK and CodePipeline to build and deploy a React application to S3. After the CodePipeline phase, in my own stack, I defined the S3 bucket like this:

const bucket = new Bucket(this, "Bucket", {
    websiteIndexDocument: "index.html",
    websiteErrorDocument: "error.html",
})

which worked. And then I defined the deployment of my built React app like this:

new BucketDeployment(this, "WebsiteDeployment", {
    sources: [Source.asset("./")],
    destinationBucket: bucket
})

which doesn't seem to work. Is that use of BucketDeployment correct?

Something odd that happens when I add the BucketDeployment lines is that cdk synth or cdk deploy, they never finish and they seem to generate an infinite recursive tree in cdk.out, so something definitely seems wrong there.

And if I change to Source.asset("./build") I get the error:

> cdk synth
C:\Users\pupeno\Code\ww3fe\node_modules\aws-cdk-lib\core\lib\asset-staging.ts:109
      throw new Error(`Cannot find asset at ${this.sourcePath}`);
            ^
Error: Cannot find asset at C:\Users\pupeno\Code\ww3fe\build
    at new AssetStaging (C:\Users\pupeno\Code\ww3fe\node_modules\aws-cdk-lib\core\lib\asset-staging.ts:109:13)
    at new Asset (C:\Users\pupeno\Code\ww3fe\node_modules\aws-cdk-lib\aws-s3-assets\lib\asset.ts:72:21)
    at Object.bind (C:\Users\pupeno\Code\ww3fe\node_modules\aws-cdk-lib\aws-s3-deployment\lib\source.ts:55:23)
    at C:\Users\pupeno\Code\ww3fe\node_modules\aws-cdk-lib\aws-s3-deployment\lib\bucket-deployment.ts:170:83
    at Array.map (<anonymous>)
    at new BucketDeployment (C:\Users\pupeno\Code\ww3fe\node_modules\aws-cdk-lib\aws-s3-deployment\lib\bucket-deployment.ts:170:51)
    at new MainStack (C:\Users\pupeno\Code\ww3fe\infra\pipeline-stack.ts:16:9)
    at new DeployStage (C:\Users\pupeno\Code\ww3fe\infra\pipeline-stack.ts:28:26)
    at new PipelineStack (C:\Users\pupeno\Code\ww3fe\infra\pipeline-stack.ts:56:24)
    at Object.<anonymous> (C:\Users\pupeno\Code\ww3fe\infra\pipeline.ts:6:1)
Subprocess exited with error 1

which would indicate this is very wrong. Why is it searching for the build directory on my machine? It's supposed to search for it in CodePipeline, after building.

My whole pipeline is:

import {Construct} from "constructs"
import {CodeBuildStep, CodePipeline, CodePipelineSource} from "aws-cdk-lib/pipelines"
import {Stage, CfnOutput, StageProps, Stack, StackProps} from "aws-cdk-lib"
import {Bucket} from "aws-cdk-lib/aws-s3"
import {BucketDeployment, Source} from "aws-cdk-lib/aws-s3-deployment"

export class MainStack extends Stack {
    constructor(scope: Construct, id: string, props?: StageProps) {
        super(scope, id, props)

        const bucket = new Bucket(this, "Bucket", {
            websiteIndexDocument: "index.html",
            websiteErrorDocument: "error.html",
        })

        new BucketDeployment(this, "WebsiteDeployment", {
            sources: [Source.asset("./")],
            destinationBucket: bucket
        })

        new CfnOutput(this, "BucketOutput", {value: bucket.bucketArn})
    }
}

export class DeployStage extends Stage {
    public readonly mainStack: MainStack

    constructor(scope: Construct, id: string, props?: StageProps) {
        super(scope, id, props)
        this.mainStack = new MainStack(this, "example")
    }
}

export class PipelineStack extends Stack {
    constructor(scope: Construct, id: string, props?: StackProps) {
        super(scope, id, props)

        const pipeline = new CodePipeline(this, id, {
            pipelineName: id,
            synth: new CodeBuildStep("Synth", {
                    input: CodePipelineSource.connection("user/example", "main", {
                        connectionArn: "arn:aws:codestar-connections:....",
                    }),
                    installCommands: [
                        "npm install -g aws-cdk"
                    ],
                    commands: [
                        "npm ci",
                        "npm run build",
                        "npx cdk synth"
                    ]
                }
            ),
        })

        const deploy = new DeployStage(this, "Staging")
        const deployStage = pipeline.addStage(deploy)
    }
}

The actual error I'm experiencing in AWS is this:

[Container] 2022/01/25 20:28:27 Phase complete: BUILD State: SUCCEEDED
[Container] 2022/01/25 20:28:27 Phase context status code:  Message: 
[Container] 2022/01/25 20:28:27 Entering phase POST_BUILD
[Container] 2022/01/25 20:28:27 Phase complete: POST_BUILD State: SUCCEEDED
[Container] 2022/01/25 20:28:27 Phase context status code:  Message: 
[Container] 2022/01/25 20:28:27 Expanding base directory path: cdk.out
[Container] 2022/01/25 20:28:27 Assembling file list
[Container] 2022/01/25 20:28:27 Expanding cdk.out
[Container] 2022/01/25 20:28:27 Skipping invalid file path cdk.out
[Container] 2022/01/25 20:28:27 Phase complete: UPLOAD_ARTIFACTS State: FAILED
[Container] 2022/01/25 20:28:27 Phase context status code: CLIENT_ERROR Message: no matching base directory path found for cdk.out

In case it matters, by cdk.json, in the root of my repo, contains:

{
  "app": "npx ts-node --project infra/tsconfig.json --prefer-ts-exts infra/pipeline.ts",
  "watch": {
    "include": [
      "**"
    ],
    "exclude": [
      "README.md",
      "cdk*.json",
      "**/*.d.ts",
      "**/*.js",
      "tsconfig.json",
      "package*.json",
      "yarn.lock",
      "node_modules",
      "test"
    ]
  },
  "context": {
    "@aws-cdk/aws-apigateway:usagePlanKeyOrderInsensitiveId": true,
    "@aws-cdk/core:stackRelativeExports": true,
    "@aws-cdk/aws-rds:lowercaseDbIdentifier": true,
    "@aws-cdk/aws-lambda:recognizeVersionProps": true,
    "@aws-cdk/aws-cloudfront:defaultSecurityPolicyTLSv1.2_2021": true
  }
}