Why can't I connect to a new AWS Aurora Serverless instance from my PC?

Trying to set up a vanilla AWS RDS Aurora Serverless instance.

For now, I just want to connect to it directly from my PC as a sanity check, but I'm unable to do so. Every time I connect via $ mysql, it hands for a few minutes. Then I get:

$ mysql -h <MY-DATABASE>.cluster-deadbeef.us-west-1.rds.amazonaws.com -P 3306 -u admin -p
ERROR 2003 (HY000): Can't connect to MySQL server on '<MY-DATABASE>.cluster-deadbeef.us-west-1.rds.amazonaws.com' (60)

(nc also just times out)

Looks like there's a network connectivity I've made somewhere, but I'm not sure where.

Here's the entire setup (think I've included everything relevant?):

• Database Instance:

  $ aws rds describe-db-clusters --output json | jq '.DBClusters[0] | {AvailabilityZones, DBSubnetGroup, VpcSecurityGroups}'
  {
    "AvailabilityZones": [
      "us-west-1c",
      "us-west-1b"
    ],
    "DBSubnetGroup": "default-vpc-0165fd69fae5d2569",
    "VpcSecurityGroups": [
      {
        "VpcSecurityGroupId": "sg-051e6ad0fe8837a56",
        "Status": "active"
      }
    ]
  }
  

• VPC:

  $ aws ec2 describe-vpcs --output json | jq '.Vpcs[0] | {VpcId, CidrBlock, CidrBlockAssociationSet}'
  {
    "VpcId": "vpc-0165fd69fae5d2569",
    "CidrBlock": "10.0.0.0/16",
    "CidrBlockAssociationSet": [
      {
        "AssociationId": "vpc-cidr-assoc-0fe35851049a94f32",
        "CidrBlock": "10.0.0.0/16",
        "CidrBlockState": {
          "State": "associated"
        }
      }
    ]
  }
  

• VPC Subnets:

  $ aws ec2 describe-subnets --output json | jq '.Subnets[] | {AvailabilityZone,AvailabilityZoneId,CidrBlock,VpcId}'  
  
  {
    "AvailabilityZone": "us-west-1c",
    "AvailabilityZoneId": "usw1-az1",
    "CidrBlock": "10.0.1.0/24",
    "VpcId": "vpc-0165fd69fae5d2569"
  }
  {
    "AvailabilityZone": "us-west-1b",
    "AvailabilityZoneId": "usw1-az3",
    "CidrBlock": "10.0.0.0/24",
    "VpcId": "vpc-0165fd69fae5d2569"
  }
  

• Security Group:

  Yes this is totally wide open for now, still can't connect :(

  $ aws ec2 describe-security-groups --output json | jq '.SecurityGroups[]'
  {
    "IpPermissions": [
      {
        "IpProtocol": "-1",
        "IpRanges": [
          {
            "CidrIp": "0.0.0.0/0"
          }
        ],
        "Ipv6Ranges": [
          {
            "CidrIpv6": "::/0"
          }
        ],
        "PrefixListIds": [],
        "UserIdGroupPairs": [
          {
            "GroupId": "sg-051e6ad0fe8837a56",
          }
        ]
      },
      {
        "FromPort": 3306,
        "IpProtocol": "tcp",
        "IpRanges": [
          {
            "CidrIp": "0.0.0.0/0"
          }
        ],
        "Ipv6Ranges": [
          {
            "CidrIpv6": "::/0"
          }
        ],
        "PrefixListIds": [],
        "ToPort": 3306,
        "UserIdGroupPairs": []
      }
    ],
    "GroupId": "sg-051e6ad0fe8837a56",
    "IpPermissionsEgress": [
      {
        "IpProtocol": "-1",
        "IpRanges": [
          {
            "CidrIp": "0.0.0.0/0"
          }
        ],
        "Ipv6Ranges": [],
        "PrefixListIds": [],
        "UserIdGroupPairs": []
      }
    ],
    "VpcId": "vpc-0165fd69fae5d2569"
  }
  

• Route Table:

  $ aws ec2 describe-route-tables --output json | jq '.RouteTables[]'   
  {
    "Associations": [
      {
        "Main": true,
        "RouteTableAssociationId": "rtbassoc-0aebc4a882b0cd2a5",
        "RouteTableId": "rtb-0ce6ee26652736941",
        "AssociationState": {
          "State": "associated"
        }
      },
      {
        "Main": false,
        "RouteTableAssociationId": "rtbassoc-047d54469da606a50",
        "RouteTableId": "rtb-0ce6ee26652736941",
        "SubnetId": "subnet-0744475e288c0424c",
        "AssociationState": {
          "State": "associated"
        }
      },
      {
        "Main": false,
        "RouteTableAssociationId": "rtbassoc-08c5ea54642014c95",
        "RouteTableId": "rtb-0ce6ee26652736941",
        "SubnetId": "subnet-0b9c99ff38b860725",
        "AssociationState": {
          "State": "associated"
        }
      }
    ],
    "RouteTableId": "rtb-0ce6ee26652736941",
    "Routes": [
      {
        "DestinationCidrBlock": "10.0.0.0/16",
        "GatewayId": "local",
        "Origin": "CreateRouteTable",
        "State": "active"
      },
      {
        "DestinationCidrBlock": "0.0.0.0/0",
        "GatewayId": "igw-0f8ad7dfe1eaa0c67",
        "Origin": "CreateRoute",
        "State": "active"
      }
    ],
    "VpcId": "vpc-0165fd69fae5d2569",
  }
  

What am I missing?

thanks!!