MIPS API pcsx_putc only output after newline

### Describe the bug

Unsure if this is a bug or just undocumented behaviour, but when i try to user `pcsx_putc` to output to the console (both in logs and when redirecting to stdout) it will only appear after you putc a newline `\n`

e.g.

```
pcsx_putc('c');
pcsx_putc('d');
```

won't output anything but

```
pcsx_putc('c');
pcsx_putc('d');
pcsx_putc('\n');
```

will output `cd` in the console

### Expected behavior

Either it should output each character or if it require a newline to "submit" all character queue till then, this should be added to the documentation

### Steps to reproduce the bug

Use the pcsx_putc function in any source code compiling to psexe. This was tested in one of the basic example of https://github.com/spicyjpeg/ps1-bare-metal

### Operating System

Windows 11

### PCSX-Redux version

Version: 22916.20250902.2.x64
Build: 270
Changeset: 718f0912a44320faf2668e71d3ce9cc3207485bd
Date & time: 2025-09-02 04:09:36

### CPU model

Intel(R) Core(TM) i7-10700 CPU @ 2.90GHz (2.90 GHz)

### GPU model & Drivers

GeForce RTX 3080, Driver : 3.2.0 NVIDIA 581.57

### BIOS version

OpenBIOS

### Options

- [ ] Dynarec CPU
- [ ] 8MB
- [ ] OpenGL GPU
- [ ] Fastboot
- [x] Debugger

### Iso checks

_No response_

### Logs

_No response_

### Additional information

_No response_