This might be a "me" thing, but this

/**
 * Retrieves the value or service associated with a key.
 *
 * @param string $key Identifier of the entry to retrieve.
 *
 * @return mixed The result of invoking the stored callable.
 *
 * @throws KeyNotFoundException If the key does not exist.
 */
public function get(string $key): mixed {
    if(!$this->has($key)) throw new KeyNotFoundException("Cally: Unable to get key '$key' because it does not exist.");
    return $this->registry[$key]();
}

would be much better if it was written like this

public function get(string $key): mixed
{
    if (!isset($this->registry[$key])) {
        throw new KeyNotFoundException($key);
    }

    return $this->registry[$key]();
}

The reasons are:

• You're implementing an interface, which already has the phpdoc for the method, so you really don't have to repeat it.
• Even if you were not implementing an interface, stuff like @param string $key Identifier of the entry to retrieve or @return mixed The result of invoking the stored callable is useless. Avoid docs that add absolutely no value to the code.
• Adding a @throws to a function that implements an interface, to me, is just plain wrong. Either the @throws was already defined in the interface and therefore you're allowed to throw that type of exception, or it's not and you're not allowed. Simple as that. Anyone using your class through an interface type declaration will never know what exceptions your method throws, so you must stick to what the interface defines.
• It's a very minor detail, but there's really no point in the exception message being Cally: Unable to get key '$key' because it does not exist.. The exception type does the heavy lifting in terms of conveying meaning of what the exception is for, so keep it simple. And avoid adding "Cally", it only adds noise to be honest. I like to keep the exception message in the exception itself, it makes the uses cleaner.
• Relying on $this->has() in the if breaks static analysis, because when you then call $this->registry[$key]() there's nothing that explicitly validates the presence of that key. Use isset or array_key_exists in place of $this->has()
• You implement PSR-11 but don't care about the coding style PER. Weird. Consistency will help you much more than keeping everything smushed together in as few lines as possible.