Several members of my closest family have experienced depressions and/or anxiety disorder. What they need most is a feeling of being accepted and supported despite their shortcommings.
First let me tell you about possible reasons why your son avoids talking about moving out.
Telling your son that he needs to move out can triger a feeling of being abandoned or cast out. That might be one reason why he reacts so strongly to your request. One of my family member has a similar anxiety of losing their job. Objectively they know their boss respects and supports them and that they are qualified enough to find a new job. But any small problem at work, any sick day they have to take due to their mental illness triggers an irrational panic of not being good enough.
A second reason can be what I call "energy leeching". Another of my family members was going through therapy a few years back and found the process extremely draining. We live in different cities, but close enough that I visited every other weekend. Once they told me that they felt like every time I visited I brought all my energy to them and that they would feel more optimistic and energized when I was visiting. Your son may feel a similar dependency to you and fear he might fall back into depression when you leave.
And last but not least, moving out takes energy. Huge amounts of energy that your son might not feel he has. To a depressed person the prospect of moving out can feel like building the Tower of Babel. One of my family members said that they know it's possible to accomplish such a task, they see other people accomplishing it, but to them it may as well be a biblical miracle that they simply don't receive. Their own lack of energy leads them to a spiral of procrastination (doing other, useless things to avoid the task at hand), followed by shame and regret, which makes them feel even more powerless and drained. The result is that it commonly takes them 3 or more weeks to make an urgent phone call.
How does this help you talking to your son?
First of all, there is not one single reason why he avoids the topic. It would help you tremendously to first talk about his feelings and motivations - or lack thereof - to understand why he blocks you.
What I found exceptionally helpfull was talking about your general state of mind without talking directly about the problem at hand. In case of the "energy leeching" incident I asked the other person how my presence makes a difference to them and told them how my frequent visits felt draining to me.
Try asking your son how he's doing, how he feels about his job, how he feels after a few free days. Then tell him the same things about you. How you feel restrained to one room inside your own home and how that is stressful to you. The goal here is to understand your son and help him understand you by comparing how you experience the current living arrangements.
Keep in mind that people with depression tend to perceive things more negatively than healthy people. So don't hesitate to assure him that you still love him and support him and want to be close to him, but that the current situation is becomming unbearable to you.
Then you should propose a solution to the problem. How exactly this looks like depends on why exactly he doesn't want to move out (see examples above).
If he's afraid to be abandoned, propose to move close by and visit each other often. Tell him he's always welcome to visit you.
Same for the "energy leeching". If you understand his needs, you can incorporate a ways to fulfill these needs into your proposed plan.
If he feels overwhelmed with the prospect of finding a new place and moving there, present him with a step-by-step plan and work on every step together with him.
A good way to overcome his anxieties that worked well in my family was to "just try things out for a while". You present your plan of moving out, but instead of a sudden change, you introduce the changes in little steps. Make it clear that this is a test run and if anything goes wrong, you can change the plan and adapt the approach.
- First talk about moving out (you already did that, but it's important to let the other person think about such drastic changes for a while).
- Stay somewhere else for a few days. Maybe you can stay with your boyfriend at the weekends but at your place during the week. This gives him time to experience living alone without the preassure that he has to master it right now.
- Slowly increase the time you stay away, maybe staying all week with your boyfriend and only at your place for 2 nights.
- Move out, but take your time with it. Take only the most important things with you, then come and grab more of your stuff each weekend.
- Call and visit your son often, even after you moved out for good.
Just knowing that there's still a chance of reverting to the old ways if anything does go wrong made my family member feel much more comfortable with the plan. There were some hard days, but in the end they didn't actually need to go back.