This will combine Http and Rest Api's into one "cache". Will we run into a issue where the key used will collide between the two different resources if they are in the same template?

The key is the logical IDs of the generated AWS::Route53::RecordSetGroup resources. For both case of Http API and Rest API, the logical ID is generated based on either HostedZoneId or HostedZoneName. So, corresponding record set would still be appended into an existing generated record set group instead of overwriting it.
I added a test for this mixed api case.

What happens in HostedZoneId is an intrinsic function?

The entire HostedZoneId is used to generate a logical ID hash of the generated RecordSet Group. For example, consider HostedZoneId: !Ref MyParam, HostedZoneId: !Sub "{{MyParam}}", and HostedZoneId: "abc123456". Even if MyParamresolves to"abc123456", these three would yield RecordSet Groups with different logical ID hashes. In the case where only one kind of intrinsics is used for HostedZoneId`, only one RecordSet Group would be generated.

In the case where multiple kinds of intrinsics are used for HostedZoneId, there is no issue at well. Multiple AWS::Route53::RecordSetGroup resources can be created in a template pointing to the same HostedZoneId. For example, the template below can be deployed without any issue:

Resources:
  HostedZone:
    Type: "AWS::Route53::HostedZone"
    Properties:
      Name: "my-website.com"

  MyRecordSetGroup1:
    Type: AWS::Route53::RecordSetGroup
    Properties:
      HostedZoneId: !Ref HostedZone
      RecordSets:
        - Name: "my-website.com"
          Type: "A"
          TTL: "900"
          ResourceRecords:
            - "101.10.21.3"

  MyRecordSetGroup2:
    Type: AWS::Route53::RecordSetGroup
    Properties:
      HostedZoneId: !Ref HostedZone
      RecordSets:
        - Name: "www.my-website.com"
          Type: "CNAME"
          TTL: "900"
          ResourceRecords:
            - "my-website.com"