flake: TestAgent_Startup/HomeDirectory

## CI Failure Details

**CI Run:** https://github.com/coder/coder/actions/runs/27441018780
**Failed Job:** https://github.com/coder/coder/actions/runs/27441018780/job/81114905940 (test-go-pg (windows-2022))
**Commit:** d6aa3d61ee4ad38b60d887641ff8084f4b676c2b (TJ) https://github.com/coder/coder/commit/d6aa3d61ee4ad38b60d887641ff8084f4b676c2b

## Failing Test

`TestAgent_Startup/HomeDirectory`

File: `agent/agent_test.go` (around line ~2249)

## Error Output (panic / timeout)

```
=== FAIL: agent (0.00s)
panic: test timed out after 20m0s
running tests:
TestAgent_Startup/HomeDirectory (19m57s)
```

## Error Analysis

The `agent` package hit the Go test watchdog timeout on Windows. The running test list shows `TestAgent_Startup/HomeDirectory` stuck for ~20 minutes, indicating a hang in startup/manifest resolution or agent setup on Windows.

## Root Cause Assessment

*Process timeout / hang* in `TestAgent_Startup/HomeDirectory` on Windows CI.

## Data Race / OOM Checks

Searched logs for `WARNING: DATA RACE`, `out of memory`, `signal: killed` — none found. Failure is a Go test timeout panic.

## Assignment Analysis

Intended blame command:
- `git blame -L 2242,2275 agent/agent_test.go`

Proxy via history (available tooling):
- `git log --oneline -10 --follow agent/agent_test.go`
- Most recent substantive change touching this area: `3955df79` ("fix(agent): unify working directory resolution") by Mathias Fredriksson.

Assigning to **@mafredri** as the most recent modifier of the working directory resolution + startup test area.

## Related Issues

Searched `coder/internal` for:
- `TestAgent_Startup` / `TestAgent_Startup/HomeDirectory`
- `agent_test.go` + `Startup`
- `test timed out after 20m` + `agent`

No matching issues found.

## Reproduction

```
go test ./agent -run TestAgent_Startup/HomeDirectory -count=1
```