Synth doesn't appear in crew manifest

### Testmerges

doesn't matter

### Round ID

doesn't matter

### Description of the bug

If you wait long enough not picking a loadout - you won't appear in crew manifest - have a vid.

https://github.com/user-attachments/assets/50bbf2ed-b552-459d-a321-a9839f0b1e85

### What's the difference with what should have happened?

I should be on the list!!!

### How do we reproduce this bug?

1. Load into the game
2. Wait
3. Wait
4. Wait
5. Be sad - you are not part of the crew, part of the ship...

### Issue Bingo

- [x] Issue could be reproduced at least once
- [x] Issue happened in a recent (less than 7 days ago) round
- [x] Couldn't find an existing issue about this (https://github.com/cmss13-devs/cmss13/issues)

Start by reproducing the issue in CM-SS13 using the reported sequence: load into the game, wait without picking a loadout, and check the crew manifest. Use the attached video and compare the expected crew listing with the observed result. Done means a player who waits without selecting a loadout still appears in the crew manifest.

Written by the indexing model from the issue text.