aws_signer: Removing tags to stack containing signing profile causes errors

### Describe the bug

https://github.com/aws/aws-cdk/issues/30013

### Regression Issue

- [ ] Select this option if this issue appears to be a regression.

### Last Known Working CDK Version

_No response_

### Expected Behavior

Error is still happening, just on removal instead of adding

### Current Behavior

Removing tag from stack causes deployment error

### Reproduction Steps

Clone github repo, deploy stack, comment out or remove tag, stack will fail to deploy

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.157.0 (build 7315a59)

### Framework Version

_No response_

### Node.js Version

v20.17.0

### OS

Ubuntu 24.04

### Language

Python

### Language Version

_No response_

### Other information

_No response_

Start with the aws_signer implementation in the AWS CDK repository and reproduce the deployment using CDK CLI 2.157.0, first with a tag and then after removing it. Compare the failure with the related issue #30013 and trace the signing-profile resource handling. Done means removing the stack tag no longer causes deployment to fail, with coverage for the removal path.

Written by the indexing model from the issue text.