Docs: Get Started fails because Postgrex Protocol fails to connect

### Code of Conduct

- [x] I agree to follow this project's Code of Conduct

### AI Policy

- [x] I agree to follow this project's AI Policy, or I agree that AI was not used while creating this issue.

### Versions

elixir 1.20.3-otp-29
erlang 29.0.5

mix deps
* ash 3.32.0 (Hex package) (mix)
locked at 3.32.0 (ash) ee80eeac
ok
* ash_phoenix 2.3.24 (Hex package) (mix)
locked at 2.3.24 (ash_phoenix) 46e3209c
ok
* bandit 1.12.5 (Hex package) (mix)
locked at 1.12.5 (bandit) c5684ca0
ok
* crux 0.1.4 (Hex package) (mix)
locked at 0.1.4 (crux) ff7d880c
ok
* daisyui (https://github.com/saadeghi/daisyui.git - v5.5.20)
locked at 22ecff5 (tag: v5.5.20)
ok
* db_connection 2.10.2 (Hex package) (mix)
locked at 2.10.2 (db_connection) 510b1448
ok
* decimal 3.1.1 (Hex package) (mix)
locked at 3.1.1 (decimal) c5f25f2c
ok
* dns_cluster 0.2.0 (Hex package) (mix)
locked at 0.2.0 (dns_cluster) ba6f1893
ok
* ecto 3.14.2 (Hex package) (mix)
locked at 3.14.2 (ecto) 25d60b8c
ok
* ecto_sql 3.14.0 (Hex package) (mix)
locked at 3.14.0 (ecto_sql) f4d8d36f
ok
* esbuild 0.10.0 (Hex package) (mix)
locked at 0.10.0 (esbuild) 468489cd
ok
* ets 0.9.0 (Hex package) (mix)
locked at 0.9.0 (ets) 2861fdfb
ok
* ex_ast 0.13.1 (Hex package) (mix)
locked at 0.13.1 (ex_ast) bd15f68c
ok
* expo 1.1.1 (Hex package) (mix)
locked at 1.1.1 (expo) 5fb308b9
ok
* file_system 1.1.1 (Hex package) (mix)
locked at 1.1.1 (file_system) 7a15ff97
ok
* finch 0.23.0 (Hex package) (mix)
locked at 0.23.0 (finch) 80e58d3f
ok
* gettext 1.0.2 (Hex package) (mix)
locked at 1.0.2 (gettext) eab80550
ok
* glob_ex 0.1.12 (Hex package) (mix)
locked at 0.1.12 (glob_ex) 2e2fac83
ok
* heroicons (https://github.com/tailwindlabs/heroicons.git - v2.2.0)
locked at 0435d4c (tag: v2.2.0)
ok
* hpax 1.0.4 (Hex package) (mix)
locked at 1.0.4 (hpax) afc7cb14
ok
* idna 7.1.0 (Hex package) (rebar3)
locked at 7.1.0 (idna) 6ae959a0
ok
* igniter 0.8.3 (Hex package) (mix)
locked at 0.8.3 (igniter) afc5e384
ok
* iterex 0.1.2 (Hex package) (mix)
locked at 0.1.2 (iterex) 2e103b8b
ok
* jason 1.4.5 (Hex package) (mix)
locked at 1.4.5 (jason) b0c82399
ok
* mime 2.0.7 (Hex package) (mix)
locked at 2.0.7 (mime) 6171188e
ok
* mint 1.9.3 (Hex package) (mix)
locked at 1.9.3 (mint) 5f7c9342
ok
* multigraph 0.16.1-mg.4 (Hex package) (mix)
locked at 0.16.1-mg.4 (multigraph) b9f3e257
ok
* nimble_options 1.1.1 (Hex package) (mix)
locked at 1.1.1 (nimble_options) 821b2470
ok
* nimble_pool 1.1.0 (Hex package) (mix)
locked at 1.1.0 (nimble_pool) af2e4e6b
ok
* owl 0.13.1 (Hex package) (mix)
locked at 0.13.1 (owl) 351e768a
ok
* phoenix 1.8.12 (Hex package) (mix)
locked at 1.8.12 (phoenix) e33bebd0
ok
* phoenix_ecto 4.7.0 (Hex package) (mix)
locked at 4.7.0 (phoenix_ecto) 1d75011e
ok
* phoenix_html 4.3.0 (Hex package) (mix)
locked at 4.3.0 (phoenix_html) 3eaa290a
ok
* phoenix_live_dashboard 0.8.7 (Hex package) (mix)
locked at 0.8.7 (phoenix_live_dashboard) 3a8625ca
ok
* phoenix_live_reload 1.7.0 (Hex package) (mix)
locked at 1.7.0 (phoenix_live_reload) dc9f4427
ok
* phoenix_live_view 1.2.10 (Hex package) (mix)
locked at 1.2.10 (phoenix_live_view) bcf9d648
ok
* phoenix_pubsub 2.2.0 (Hex package) (mix)
locked at 2.2.0 (phoenix_pubsub) adc313a5
ok
* phoenix_template 1.0.4 (Hex package) (mix)
locked at 1.0.4 (phoenix_template) 2c0c81f0
ok
* plug 1.20.3 (Hex package) (mix)
locked at 1.20.3 (plug) be266aee
ok
* plug_crypto 2.2.0 (Hex package) (mix)
locked at 2.2.0 (plug_crypto) 83a95744
ok
* postgrex 0.22.4 (Hex package) (mix)
locked at 0.22.4 (postgrex) 4aae45a2
ok
* reactor 1.0.6 (Hex package) (mix)
locked at 1.0.6 (reactor) e3f8fd8e
ok
* req 0.7.3 (Hex package) (mix)
locked at 0.7.3 (req) 73b30303
ok
* rewrite 1.3.0 (Hex package) (mix)
locked at 1.3.0 (rewrite) d111ac7f
ok
* sourceror 1.12.2 (Hex package) (mix)
locked at 1.12.2 (sourceror) da37d3da
ok
* spark 2.7.2 (Hex package) (mix)
locked at 2.7.2 (spark) adb323dd
ok
* spitfire 0.4.0 (Hex package) (mix)
locked at 0.4.0 (spitfire) 7e5c6d15
ok
* splode 0.3.2 (Hex package) (mix)
locked at 0.3.2 (splode) 08fd658f
ok
* stream_data 1.4.0 (Hex package) (mix)
locked at 1.4.0 (stream_data) 2b0ee3a3
ok
* swoosh 1.27.1 (Hex package) (mix)
locked at 1.27.1 (swoosh) 9e732f46
ok
* tailwind 0.5.1 (Hex package) (mix)
locked at 0.5.1 (tailwind) c4e26302
ok
* telemetry 1.4.2 (Hex package) (rebar3)
locked at 1.4.2 (telemetry) 928f6495
ok
* telemetry_metrics 1.1.0 (Hex package) (mix)
locked at 1.1.0 (telemetry_metrics) e7b79e8d
ok
* telemetry_poller 1.3.0 (Hex package) (rebar3)
locked at 1.3.0 (telemetry_poller) 51f18bed
ok
* text_diff 0.1.0 (Hex package) (mix)
locked at 0.1.0 (text_diff) d1ffaaec
ok
* thousand_island 1.5.0 (Hex package) (mix)
locked at 1.5.0 (thousand_island) 708923d4
ok
* websock 0.5.3 (Hex package) (mix)
locked at 0.5.3 (websock) 6105453d
ok
* websock_adapter 0.6.0 (Hex package) (mix)
locked at 0.6.0 (websock_adapter) 50021a85
ok
* yamerl 0.10.0 (Hex package) (rebar3)
locked at 0.10.0 (yamerl) 346adb29
ok
* yaml_elixir 2.12.2 (Hex package) (mix)
locked at 2.12.2 (yaml_elixir) e7c1b101
ok
* ymlr 5.1.6 (Hex package) (mix)
locked at 5.1.6 (ymlr) b36d7c72
ok

### Operating system

Debian 13.6 (same problem with Ubuntu 24.04.4 LTS running in WSL)

### Current Behavior

While working through the Get Started tutorial a problem arises in [Try our first resource out](https://ash.hexdocs.pm/get-started.html#try-our-first-resource-out).

`iex` starts and compiles lots of code. Then it repeats a `Postgrex Protocol` error message continuously. Eventually the `iex` prompt appears, but the `Postgrex Protocol` error messages continue.

```
joel@try-ash:~/helpdesk$ iex -S mix
Erlang/OTP 29 [erts-17.0.5] [source] [64-bit] [smp:12:1] [ds:12:1:10] [async-threads:1] [jit:ns]

[Compilation messages omitted]

[error] `inotify-tools` is needed to run `file_system` for your system, check https://github.com/rvoicilas/inotify-tools/wiki for more information about how to install it. If it's already installed but not be found, appoint executable file with `config.exs` or `FILESYSTEM_FSINOTIFY_EXECUTABLE_FILE` env.
[warning] Not able to start file_system worker, reason: {:error, :fs_inotify_bootstrap_error}
[warning] Could not start Phoenix live-reload because we cannot listen to the file system.
You don't need to worry! This is an optional feature used during development to
refresh your browser when you save files and it does not affect production.

[error] Postgrex.Protocol (#PID<0.411.0> ("db_conn_2")) failed to connect: ** (DBConnection.ConnectionError) tcp connect (localhost:5432): connection refused - :econnrefused
[error] Postgrex.Protocol (#PID<0.412.0> ("db_conn_3")) failed to connect: ** (DBConnection.ConnectionError) tcp connect (localhost:5432): connection refused - :econnrefused
[error] Postgrex.Protocol (#PID<0.413.0> ("db_conn_4")) failed to connect: ** (DBConnection.ConnectionError) tcp connect (localhost:5432): connection refused - :econnrefused
Interactive Elixir (1.20.3) - press Ctrl+C to exit (type h() ENTER for help)
[error] Postgrex.Protocol (#PID<0.410.0> ("db_conn_1")) failed to connect: ** (DBConnection.ConnectionError) tcp connect (localhost:5432): connection refused - :econnrefused
iex(1)>
BREAK: (a)bort (A)bort with dump (c)ontinue (p)roc info (i)nfo
(l)oaded (v)ersion (k)ill (D)b-tables (d)istribution
```

### Reproduction

Working as user `joel` in a new Proxmox LXC container running Debian 13.6 ...

### Install Erlang and Elixir
Install Erlang and Elixir prerequisites.

```
sudo apt-get install -y \
build-essential autoconf automake libncurses-dev \
libssl-dev libwxgtk3.2-dev xsltproc fop libxml2-utils \
unixodbc-dev default-jdk flex bison
```

Install and activate Mise

```
curl https://mise.run | sh
echo 'eval "$(~/.local/bin/mise activate bash)"' >> ~/.bashrc
```

Restart the shell session.

```
exec bash -l
```

Install Erlang and Elixir.

```
mise install erlang@latest && mise use erlang@latest
mise install elixir@latest && mise use elixir@latest
```

Check the installation.

```
mise doctor
mise ls
```
### Follow the Get Started Tutorial
Install `phx.new` and `igniter_new`.
```
mix archive.install hex phx_new
mix archive.install hex igniter_new
```
Create a new Phoenix project.
```
mix igniter.new helpdesk --install ash,ash_phoenix --with phx.new
```
Copy code from Getting Started into `ticket.ex` and `support.ex`.
```
cd helpdesk
mkdir -p lib/helpdesk/support
cat > lib/helpdesk/support/ticket.ex
...
cat > lib/helpdesk/support.ex
...
```
Add this line to `config/config.exs`.
```
config :helpdesk, :ash_domains, [Helpdesk.Support]
```
Try out the first resource.
```
iex -S mix
```

### Expected Behavior

Expected `iex` to compile code and present a prompt so I could continue the tutorial.

Start with the linked Get Started section, especially “Try our first resource out,” and reproduce the issue with `iex -S mix` after reviewing the shown `ticket.ex`, `support.ex`, and `config/config.exs` steps. Determine what setup guidance is missing for the Postgrex connection and verify that the documented flow reaches the IEx prompt without repeated connection errors.

Written by the indexing model from the issue text.