How much I have saved up for moving out

I have a good amount saved right now as I am thinkng about moving in with my boyfriend as he gears up to buy a house. We already talked about finances. I’m 26 and he is 27 and we both still live with our parents but trying to save and plan.

Anyway I have about 13000 saved long term so far, around 4,000 for emergencies and an additional fund as well.

I also save 23 percent of my income for retirement on top of 200 a month that goes into a Roth IRA. I’m able to do this because I still live at home.

Anyway, I also save 60 dollars every other week into my emergency fund, and 25 dollars every other week into my long term savings.

I recently just opened another savings account with Marcus Goldsmith Sachs which has a .50 percent annual percentage and I read it was good so I’m hoping to save some money each month in there and to watch that grow.

Is this a good plan? Do I have enough or a good amount?