My work is temporary so always 3, 6 or 9 months at a company before moving to the next one so I know all about moving cities for work.
I wish I could tell you something that would make the process easier, but it's still hard for me. What I can tell you is that you'll gradually build up new routines so the initial week or two will be the worst, but things will snap into place more as time goes on.
I always split my time and focus on one thing at a time. First is somewhere to live. Once I have that I sort out a way of getting back to my permanent home at the weekend. Then I focus on finding a gym. Then I focus on a supermarket and shopping routine. Those things probably aren't all relevant to you, but that's how I tackle it mentally. A routine to work out my routines
So I know it's anxiety inducing but that is only temporary...with each week that passes you'll feel better and better and before long your new life will be your new normal.