Simple health check on simple service doesn't work

#### Overview of the Issue

Can't seem to make a simple service health check work. I register it through Python's request lib, then make an endpoint available for health checks, but service checks show failing on UI.

#### Reproduction Steps

1. Start and register the service

```python
payload = {
'Address': '127.0.0.1',
'Check': {
'DeregisterCriticalServiceAfter': '30s',
'HTTP': 'http://127.0.0.1:5000',
'Interval': '5s',
'Timeout': '5s'},
'ID': 'my-service',
'Name': 'MyService',
'Port': 5000,
'Tags': ['greeter']
}

response = requests.put('http://127.0.0.1:8500/v1/agent/service/register', json=payload)
```

Testing the service manually:
```bash
>>> curl -i http://127.0.0.1:5000/health
HTTP/1.1 200 OK
date: Sun, 01 Dec 2024 04:45:37 GMT
server: uvicorn
content-length: 20
content-type: application/json

"Service is healthy"%

>>> curl -i http://127.0.0.1:5000/
HTTP/1.1 200 OK
date: Sun, 01 Dec 2024 04:45:55 GMT
server: uvicorn
content-length: 15
content-type: application/json

"Hello, world!"%
```

And in the UI:


also, after 30 seconds the service gets removed.

### Consul info for both Client and Server

Client info
agent:
check_monitors = 0
check_ttls = 0
checks = 0
services = 0
build:
prerelease =
revision = c3f767b1
version = 1.15.4
version_metadata =
consul:
acl = disabled
bootstrap = false
known_datacenters = 1
leader = true
leader_addr = 127.0.0.1:8300
server = true
raft:
applied_index = 1145
commit_index = 1145
fsm_pending = 0
last_contact = 0
last_log_index = 1145
last_log_term = 2
last_snapshot_index = 0
last_snapshot_term = 0
latest_configuration = [{Suffrage:Voter ID:b28fa40e-ec1e-21d4-5cd7-dddbd20769b0 Address:127.0.0.1:8300}]
latest_configuration_index = 0
num_peers = 0
protocol_version = 3
protocol_version_max = 3
protocol_version_min = 0
snapshot_version_max = 1
snapshot_version_min = 0
state = Leader
term = 2
runtime:
arch = amd64
cpu_count = 16
goroutines = 145
max_procs = 16
os = linux
version = go1.20.4
serf_lan:
coordinate_resets = 0
encrypted = false
event_queue = 1
event_time = 2
failed = 0
health_score = 0
intent_queue = 0
left = 0
member_time = 1
members = 1
query_queue = 0
query_time = 1
serf_wan:
coordinate_resets = 0
encrypted = false
event_queue = 0
event_time = 1
failed = 0
health_score = 0
intent_queue = 0
left = 0
member_time = 1
members = 1
query_queue = 0
query_time = 1

### Operating system and Environment details

Operating System:
Platform: linux - OpenSuse Tumbleweed
Arch: x64
Version: #1 SMP PREEMPT_DYNAMIC Wed Sep 25 07:09:20 UTC 2024 (b87e886)
Available memory (MB): 31961
Available CPU cores: 16

### Log Fragments

Don't know how

Start by reproducing the registration through the /v1/agent/service/register API with the supplied Python request and compare the configured HTTP check URL with the service endpoints and Consul UI status. Inspect the agent's health-check behavior and logs; done means the check reports passing and the service is not deregistered after 30 seconds.

Written by the indexing model from the issue text.