That sucks. It sounds like you have every reason to be angry/upset/sad/disappointed/etc. Unfortunately, while are all real and given what you've said also reasonable reactions, they just get in the way here. The company doesn't have any responsibility to let you have the same arrangement as the other person. As other people have said, the other person could have issued an ultimatum that they acceded to, or they could have a medical reason, or something else.
@obstinate is absolutely correct about the "but
he got to do X, why can't I?" being a really bad look.
Unfortunately, the way most work environments are set up the employees can make requests for changes to the work environment, but usually the company can reject them for any reason without giving the employees an explanation. You asked how they can reject this without talking to you - they just can. Even if they had agreed to it in the past, they don't need to justify changing their answer. Getting mad at the system is totally reasonable, but by itself doesn't fix the problem in any way. While anger and frustration won't get you what you want, there are ways you might be able to get what you want. You can convince the leadership why it makes sense to allow you to work from home. It sounds as though that's what you're focused on. Higher efficiency, keeping high performing employees happy, etc. are all good reasons but they might not convince the higher ups. I've seen it happen far too often that someone has a great idea but it still gets shot down. Frustrating, yes. Unusual, no. Honestly, I've seen these requests denied for all sorts of reasons - from being an opportunity to get rid of employees we wanted to see leave anyway to simply not wanting to deal with the paperwork and hassle of managing remote employees.
Most times I encountered situations similar to this during my ~15 years as a manager and/or tech lead, it took a real belief on the company's side that they were going to lose an employee that they wanted to keep for them to make a change. In many cases we decided the employee could be replaced more easily than the request could be accommodated. I think the wrong decision was made many times, but that's what I saw. Far too often higher-ups think of people as interchangeable. My company's management believed that once someone gets to the point that they're looking elsewhere, the bond of trust had already been broken and whatever happened the employee would leave even if we accommodated the request. Bottom line - even if it seems really obvious to you that the best answer all around is for them to let you work remotely, for whatever reason they aren't going to allow it unless they have a reason to change their minds - and once they've decided it's really hard to make them change the answer. So the goal is to make it easier for them to change. I think there are only 2 ways to do that. One is to just convince them, but it sounds like you've already tried that and it didn't work. The other way is to threaten to quit, but this has to be done very very carefully if you want to stay - and you have to really be ready to leave. You have to quit in a way that makes them believe the bonds between you and the company are not too frayed to repair.
My recommendation is to take two independent paths at the same time. Meet with your management on Tuesday and in that meeting be a team player who wants to help the company - NOT a disgruntled employee who is asking for something special. The attitude should be, "Living apart from my SO is significantly impacting me, but I love working for this company and I'm sure we can work together to find a way to resolve this that works for everyone and improves the company." Don't come across as angry/disgruntled/frustrated/etc., no matter how justified those feelings are or what they say to shut you up. Because they've already given you a "no", the odds that your meeting will result in an immediate change are almost zero. They are probably coming in to the meeting having already discussed between themselves that they can't change the answer; they're probably dug in. Of course if they change their answer - great! And certainly make your case and answer questions, but the goal of this meeting *is not* to get them to give you a yes. It's to make it clear to them that you are a good employee with a reasonable request, and it's also to better understand why they said no. You're laying the groundwork for later and showing that you're someone they want to hold onto because you still care about the company. At this meeting and in future interactions, really try to figure out how to make telework more palatable to them and keep being a great worker. Don't grumble, don't make snide comments that Bob gets to work remotely, don't bring up what they said in the interview, just be someone they want to hold onto. Make them want to keep you, and make them think you're not too disgruntled to hold onto.
At the same time, start looking. I know you don't want to, but you may surprise yourself and find something better. If you do - great! At that point (or when staying is simply untenable) make the request one more time, and make it good. Document it. Make sure you explain why it would benefit the company. If you've laid the groundwork that you're committed to trying to find a solution, then you've made it easier for them to change their minds. If they say no, you have a choice. You can either accept that you're not going to get what you want and stay, or you can write a resignation letter. It should be brief, but state something like, "Working at XYZ has truly been the highlight of my career. My manager (name) and <my team name> have been wonderful to work with, and management is moving the company in the right direction. I will be excited to see great things happen at XYZ in the coming months and years. Unfortunately the commute to (nearby town) to see my SO/family/whatever has created too much of a burden and is impacting my ability to do my best work for XYZ. My last day with XYZ will be <date 2 weeks in the future>." If they value you and if you've made your case that you really can do your work remotely, they'll run to your cubicle to try to get you to stay. However, and this is the most important part, you have to be ready for them to let you leave. A resignation letter cannot be a bluff that you're not ok with them calling. When you give the letter to your manager, make it clear that you're disappointed and that you love the company, but you understand their decision (even if you don't).
The benefits of this approach are that if you don't find something better you won't have burned any bridges (if you leave) and they won't have you on a list of disgruntled employees looking to leave (if you don't). You can continue to look for something else and if/when that happens then they will want to try to work to keep you.
Finally, I usually saw people in this situation expect everything to be fixed overnight. You already understand this because it has already been and is likely to still be a months-long process. I realize that not renewing your lease complicates things, but right now tenants who can pay their lease are in a super powerful position. I bet you could extend month-to-month or for a few months for a song right now.
Good luck. I really hope this works out for you.