`@export_tool_button` breaks when changing the script contents (lambda hot-reloading)

### Tested versions

- Reproducible in 4.4dev3, the web editor

### System information

I'm running MacOS, Firefox, web editor

### Issue description

After adding a new `@export_tool_button` to a script, all tool buttons break. Seems to be fixable only by reloading the entire project.

### Steps to reproduce

My script:

```gdscript
@tool
extends Node

@export_tool_button("Hello world")
var hello_world := func():
print("Hello world")
```

The button appears in the UI. When I click it, the error message appears:

```
The value of property "hello_world" is Nil, but Callable was expected.
```

"Soft reload tool script" doesn't help.

After reloading the whole project though, it works as expected:

```
Hello world
```

But add another tool button, and both of them break again:

```gdscript
@tool
extends Node

@export_tool_button("Hello world")
var hello_world := func():
print("Hello world")

@export_tool_button("Hello world2")
var hello_world2 := func():
print("Hello world2")
```

Now the first one errors with

```
Tool button action "" is an invalid callable.
```

and the second one errors with

```
The value of property "hello_world2" is Nil, but Callable was expected.
```

Reloading the whole project again, again, fixes both problems.

### Minimal reproduction project (MRP)

Sorry I couldn't figure out how to attach the web project, and I running out of time right now.
It's basically the default project with just one scene and one script, that I pasted above.
I'm confident this will show up in any project.

Start with the provided @tool script in Godot 4.4dev3 and reproduce the failure in the web editor after adding an @export_tool_button. Investigate the soft-reload path for script contents and lambda callables. Done means existing and newly added tool buttons remain valid and callable without reloading the whole project.

Written by the indexing model from the issue text.