Not really a project but I'm apartment hunting and it's a drag. I'm far enough out from the move where I can't really do anything but make lists of complexes to follow up on later. There are some decent rate cuts due to covid and I'm super tempted to lock in an apartment early and pay double rent for a bit but that would wipe out any rent savings to be had. So all I can do is make lists and start getting rid of stuff in anticipation of the move.
I think you could reasonably call it a project. After all, it involves money and physical labor that produces a tangible object (a place to live).
Is there a lot of competition for apartments in your area? Is the vacancy rate low? If the answer to either of these is yes, then you should at least talk to the landlords or rental companies and let them know you're searching. That way you'll be known to them and even if they don't have anything suitable for you right away (or you're not moving right away), they might steer you to suites ahead of other clients or you might be able to negotiate a better deal (with incentives or perks) if they already know you.
With my own situation, I have the advantage of being known to the manager and leasing agent, and some of the maintenance staff and security. They all know I'm quiet, don't do drugs, and the one time the cops had to come here that involved me was not my fault (another tenant tried pushing his way in here after midnight and when I called customer service to make a security report, they told me to call the cops as well; security did a better job of handling the situation than the cops did). I've tried to be a good neighbor over the years, helping when I could and pointing out when something around the building needed to be fixed or changed because it was unsafe for the mobility-impaired tenants, and that does help.
Being a long-time tenant in this building (over 7 years), I'm entitled to some breaks the newer tenants don't get, like complimentary carpet steaming, and I get to keep my parking space (that I share with one other tenant since I don't have a vehicle, she and her husband have two, and they won't lower my rent if I give the space up; my housekeeping helper is also allowed to park there and have a key to the building, which is something negotiated with the previous manager).
The deal I negotiated with the manager for this move means I don't have to be out of my current apartment until October 23, and they're scheduled to finish the repairs on the place I'm moving into on September 30. So that still gives me an entire month to pack, and he said I could have the keys to the new place on October 1 as he knows it's going to take a long time for me to move my smaller things (which I'm doing to save $$$$ on the movers; that's going to take a lot of trips, 2 bankers' boxes at a time on my walker, but it's how I did my last move). I've also been promised the help of 2 of the staff here for 2 hours to help with the heavier stuff that I can't handle, and with some of my safety things. Ideally the movers will just need to deal with the extremely heavy or difficult things that I would never trust to anyone but a professional. I'd trust the local guys to move a basic dresser, but nothing breakable or fragile or electronic. That's best left to the pros.
As a result, while I didn't get the suite I wanted on the top floor, I did get one that's workable, and I've been allowed to dictate most of the changes I want made (or that I don't want made, to avoid it being classed as an upgraded suite that would cost more than I can afford). I told the manager that I care more about function than aesthetics (like don't harp on the color of the doors matching the walls; if I could have exactly what I wanted, the walls would be painted light green and I'd have wood doors and absolutely nothing here would be beige). When I still lived in the family home, we had wood paneling, wallpaper with a grey brick/ivy motif, and while the carpet was a shade of brown, that was the best compromise we did at the time it was installed, to accommodate the variety of shades of cat and dog hair that would be shed on it. Maddy is black, the carpet is beige, so it doesn't match at all here. I am most relaxed surrounded by nature colors, not some bland designer's black/white/beige idea of what "goes with everything".
So, to sum up, I suggest that when you find places you like, contact the landlord or leasing agent, and let them know you're interested in the location and approximately when. If you aren't ready to move quite yet, ask them to keep you informed of when new vacancies are about to be available (they should know these things at least 30 days in advance of anything being posted online or in the newspaper). They may be able to suggest possibilities that you would never find on your own.