[v2 Bug] `show --inline` with dbt functions (udfs) errors with `Function ... not found in project. Searched for ...`

### Is this a new bug in dbt v2.x compared to the latest version of dbt 1.x?

- [x] I believe this is a new bug in dbt v2.x
- [x] I have searched the existing issues and could not find a duplicate

### Current Behavior

As per title, `--show inline` with udfs (https://docs.getdbt.com/docs/build/udfs?version=2) don't work as expected in v2 - this causes the "highlight line to preview" functionality to fail in dbt Studio.

### Expected Behavior

No errors.

### Steps To Reproduce

```yaml
# dbt_project.yml
name: dbt_basic_5
profile: sf
version: "1.0.0"

models:
dbt_basic_5:
+materialized: table

# functions/is_pos_int.yml
functions:
- name: is_pos_int # required
config:
volatility: deterministic
arguments: # optional
- name: a_string # required if arguments is specified
data_type: string # required if arguments is specified
description: The string that I want to check if it's representing a positive integer (like "10")
default_value: "'1'" # optional, available in Snowflake and Postgres
returns: # required
data_type: integer # required
```

```sql
-- functions/is_pos_int.sql
REGEXP_INSTR(a_string, '^[0-9]+$')

-- models/foo.sql
with x as (select 1 c) select {{ function('is_pos_int') }}(c) as is_pos_int from x
```

Build

```sh
$ dbtf build && dbtf show -s foo
dbt-fusion 2.0.0-preview.209
Loading profiles.yml
Succeeded [ 0.55s] function dbt_jyeo.is_pos_int (function)
Succeeded [ 10.09s] model dbt_jyeo.foo (table)

============================ Execution Summary =============================
Finished 'build' successfully for target 'dev' [16.5s]
Processed: 1 model | 1 function
Summary: 2 total | 2 success
dbt-fusion 2.0.0-preview.209
Loading profiles.yml
Query show_model_dbt_basic_5_foo
┌────────────┐
│ IS_POS_INT │
╞════════════╡
│ 1 │
└────────────┘
1 rows.
Succeeded [ 0.79s] model dbt_jyeo.foo (table)

=========================================== Execution Summary ============================================
Finished 'show' successfully for target 'dev' [3.7s]
```

Do an inline show:

```sh
$ dbtf show --inline "with x as (select 1 c) select {{ function('is_pos_int') }}(c) as is_pos_int from x"

dbt-fusion 2.0.0-preview.209
Loading profiles.yml

========================================== Errors and Warnings ===========================================
[error] [InvalidConfig (dbt1005)]: Function 'is_pos_int' not found in project. Searched for '.is_pos_int'
--> inline_fd677450.sql:1:31

=========================================== Execution Summary ============================================
Finished 'show' with 1 error for target 'dev' [670ms]
```

Inline show with dbt-core/v1:

```sh
$ dbt show --inline "with x as (select 1 c) select {{ function('is_pos_int') }}(c) as is_pos_int from x"

21:02:58 Running with dbt=1.11.11
21:02:59 State adapter: dbt-state v2.37.1 is disabled
21:02:59 Registered adapter: snowflake=1.11.5
21:02:59 Unable to do partial parsing because an error occurred. Switching to full reparse.
21:03:00 Found 1 model, 1 sql operation, 536 macros
21:03:00
21:03:00 Concurrency: 10 threads (target='dev')
21:03:00
Previewing inline node:
| IS_POS_INT |
| ---------- |
| 1 |
```

### Relevant log output

```shell

```

### Environment

```markdown
- OS: macOS
- CPU: ARM
- dbt distribution and version: (`dbt --version`)
dbt-fusion 2.0.0-preview.209
```

### Which database adapter are you using?

snowflake

### Is this a discrepancy vs. dbt 1.x?

- [x] Yes — this works in dbt 1.x but not in dbt v2.x

### Additional Context

Fidget RCA:

This is an error-code asymmetry between ref() and function(), not a function()-specific parse bug.

Compile/Preview on a highlighted selection or unsaved buffer routes through the LSP inline path (WorkspaceMessage::Show → run_inline_show → render_sql), which renders the buffer text against the last-saved project index rather than re-parsing. When a dependency in the buffer isn't in that saved index, ref() and function() diverge:

ref() miss → lookup_ref returns DependencyNotFound (dbt1048)

function() miss → lookup_function returns InvalidConfig (dbt1005) — the exact code in this ticket

The graceful fallback is gated purely on the error code. downgraded_node_dependency_warning only downgrades DisabledDependency and DependencyNotFound to a warning (NodeNotFoundOrDisabled / dbt1087); every other code returns None and stays a hard error:

{code}
let has_disabled_or_missing_dependency = match error.code {
ErrorCode::DisabledDependency | ErrorCode::DependencyNotFound => true,
_ => return None,
};
{code}

So ref() (1048) is eligible for downgrade and falls back with a warning; function() (1005) is not eligible and hard-fails. That is the entire asymmetry.

Why the working combination works: saved + nothing-highlighted compiles the real saved node, whose function() dependency is already resolved into the index, so the lookup hits and never reaches the error branch. Command-bar dbt compile --select works for the same reason — it bypasses the inline buffer path entirely. Both match the workarounds already documented in this ticket. This is also why the behavior is adapter-agnostic (BigQuery + Snowflake) — the divergence is in dependency resolution, upstream of any adapter code.

Source references

Downgrade gate (node_resolver.rs#L39-L42): https://github.com/dbt-labs/fs/blob/7e9baadb2137aeea6a663c357fc38fbc6fba5b8d/fs/sa/crates/dbt-jinja-utils/src/node_resolver.rs#L39-L42

lookup_ref miss → dbt1048 (node_resolver.rs#L592-L597): https://github.com/dbt-labs/fs/blob/7e9baadb2137aeea6a663c357fc38fbc6fba5b8d/fs/sa/crates/dbt-jinja-utils/src/node_resolver.rs#L592-L597

lookup_function miss → dbt1005 (node_resolver.rs#L742-L749): https://github.com/dbt-labs/fs/blob/7e9baadb2137aeea6a663c357fc38fbc6fba5b8d/fs/sa/crates/dbt-jinja-utils/src/node_resolver.rs#L742-L749

Error codes InvalidConfig = 1005, DependencyNotFound = 1048 (codes.rs#L41-L85): https://github.com/dbt-labs/fs/blob/7e9baadb2137aeea6a663c357fc38fbc6fba5b8d/fs/sa/crates/dbt-error/src/codes.rs#L41-L85

Inline render resolves "ref(), source(), macros" — function() not mentioned (handler.rs#L42-L45): https://github.com/dbt-labs/fs/blob/7e9baadb2137aeea6a663c357fc38fbc6fba5b8d/crates/dbt-lsp/src/show/handler.rs#L42-L45

Likely fix direction (for Fusion engineering): make lookup_function's not-found case downgrade-eligible like ref()/source() — either give it a distinct not-found error code that gets added to the downgrade set, or stop reusing the generic InvalidConfig. Note a blanket downgrade of InvalidConfig (1005) would be wrong, since that code is also used for genuinely fatal cases such as ambiguous refs.