Restructure the logic in AssetServer::load_internal to avoid using weak handles.

[andriyDev]

Objective

• A step towards "Always Strong" Asset Handles / Remove asset weak handles #19024.
• The logic here was kinda complex before.

Solution

• I've restructured the logic here while preserving the behavior (as far as I can tell).
• We no longer return the handle if it was passed in. The caller should already have access to it, and the returned handle will be a weak handle, not a strong handle (which can cause issues). This prevents us from needing weak handles at all here.
• I verified the callers do not need the return value. The only callsite that needs the returned handle does not pass in the input_handle argument.

Testing

• CI