Depressed girlfriend overwhelmed and needs space

[26M] have a long distance relationship with a [28F] for 8 months now, and things has gone swimmingly, we visited eachother whenever we get the chance, and it's been the healthiest, happiest relationship i've ever been in. Not so long ago, we agreed to try and close the gap between us, and we agreed on me trying to move to her (London) for the past months, Brexit makes it hard unfortunately.

However, due to alot of situations in her life right now she developed depression. It scared me how quickly she changed, from texts everyday to almost nothing at all. She's says she's overwhelmed right now with multiple situations in her life such as work-stress, moving to another flat, an expensive surgery in february, and missing her mother who lives overseas.

She says all she's done lately is work, eat and sleep. She's numb, she doesn't have the energy to speak to either me, her friends, or her flatmates.

It's scary how fast the communication went from daily to almost nothing. She says she feels bad about ignoring my texts for hours, and not being able to match my energy romantically or friendly. I say it's okay because i've been where she is right now, i isolated myself during my depressive periods years ago aswell.

She says she just feels numb and overwhelmed, nothing else.

Just before this weekend she texted me apologising, she feels bad about not being able to function in the relationship right now, and that she needed space. She said earlier that our long distance situation caused her stress, but she didn't want to break up, so i just have to trust her.

I said i respected her decision. And that i'd give her the space she needs, but that i would check up on her every now and then just so see that she's okay, that i love her, and i'm here for her, and i'm not going anywhere.

I haven't heard from her in 4 days, i know she's busy moving in to her new flat, but i'm anxious about her. I try to not take it personally, i know it is the depression speaking. And i know there's nothing i can do to 'fix' her depression rather than listening and supporting, but it hurts when she pushes me away, because i want to be there for her on her bad days just as well as the good ones, she said she's going to look into therapy once she's settled into her new flat, which is a big step and which i'm super proud of.

What i'm asking here i suppose, is do you push your SO's away and needs space during depressive periods?

I know the feeling of numbness goes away after a while towards friends, but what about partners,m

Any advice for more i can do to support her? She is truly fantastic and i'm not giving up on us as long as she doesn't. I don't want to lose this amazing person and all i want is her to come back to me.