I think your manager is being unfairly harsh, but it's not going to be easy to override their decision without taking legal action.
For reference: I am a software development consultant in Belgium, working in a similar situation as yours (though I'm not in the middle of a transfer).
It's not unfair of you to talk to your manager, mention the favor you did for them by staying longer, and seeing whether they reevaluate their decision or not.
They are not required to comply with your request. You should not address this in an official capacity, as you're essentially asking for a favor.
But if they flat out refuse, that's pretty much puts a stop to any interpersonal or informal approach.
Your situation is no different (legally speaking) from leaving Alpha to go work for an unrelated company Zulu. You are officially in your notice period, any existing agreement between Alpha and Bravo is irrelevant.
However, the same rules for denying a leave application applies. An employer is allowed to deny your leave within reason.
Dutch (Belgian) reference material from the employer's perspective, translation mine:
You can deny an employee's request for paid time off. If you want them to be present on a specific day for the hand-off of information to the employee who will replace them, then you are free to deny the employee leave for that day.
However, this entails a valid justification for denying leave in a specific period. Your manager's argument is that it costs Alpha billing days. That is not a reasonable argument (in my opinion), since literally every work day is a billing day. Your employer must be prepared for your reasonable absences, and you are not expected to suffer (and be denied leave) because of their inability to do so.
So then the question becomes: when can an employer reasonably deny a leave application, and when can he not?
Dutch (Belgian) resource about leave applications, translation mine:
If you and your employer cannot agree on your leave planning, then you will have to take it to court (arbeidsrechtbank).
Nowhere in the law is it stipulated when an employer is or isn't allowed to deny a leave application; it also doesn't stipulate when planned leave can be witdrawn.
Based on legal precedents, an employer is realistically capable of (and allowed to) deny a leave application, when the interests of the company (e.g. the employee's absence would compromise the operational stability of the company) reasonably outweighs the interests of the employee. In other words, the company's benefit (by denying the leave application) must outweigh the employee's benefit (when the leave would be granted). In these cases, the court is expected to make a fair ruling.
In other words, there's not much you can do except take legal action. Before you do so, always consult with your union first.
Especially in Belgium, the union can add a considerable amount of leverage in your favor, which incentivizes your employer to avoid taking this to court.
But again, that's pretty much the only option you have here. Because it's so different for different sectors, there isn't much in the way of established legislature regarding leave applications; and the system generally operates on mutual agreement between the employer and employee; based on the general idea that both parties would prefer to avoid legal escalation, and is therefore incentivized to keep things mutually agreeable.
Here's what I would suggest:
- Talk to your manager on a personal level. Don't expect a favor, but simply ask if it's possible to get that leave anyway. I get the feeling they are already at the point of denying this, but at least you can say you tried, if this escalates further.
- Evaluate the benefits of the employer (billing hours) and the benefit to you, e.g. there is a reasonable difference between taking leave for a specific circumstance, compared to taking leave just because you want a bit of leave. Officially, you're not required to justify why you want leave, but it can help you make your case.
- Speak to your manager, and ask for their official justification (they need one). If they return the same "billing hours" argument; address the fact that this applies to literally any work day, and is not a valid justification in and of itself.
- If there's still no response (nor compromise), talk to the union. They will likely do much of the leg work for you from this point.
- If the union can't help you themselves, they'll likely assist with legal counsel if you wish to take legal steps.
- While the favor you did them (by staying longer) doesn't help you in an administrative sense, make sure to let the court know that this favor was given. It essentially invalidates any argument that your employer can make that they were relying on your presence (because you could just as well have refused to stay any longer).
Make sure you dot your T's and cross your I's, starting frmo the first bullet point. If this is more than just an accidental mistake on the employer's side, then they will likely be ready to defeat your argument by pointing at anything you did wrong.
Lesson for the future:
Next time, get your employer to agree to certain leave days at the same time as you agree to stay longer. This prevents the issue from happening; and sometimes, employers (and, to be fair, employees) can start holding grudges near the end of an otherwise friendly employment period.