My advice is that everything is going to be far more expensive than you expect, so hold on to your current situation as long as you can tolerate it (and until your finances settle out post-baby and you know how much $$ you're actually dealing with longer-term).
We are currently rebuilding post-fire, and I cannot tell you how unexpectedly high the costs are. There are still supply chain impacts from Covid, which is decreasing availability of various choices and raising the prices of those that remain. Contractors in my area remain slammed; our current guy is going to be charging literally a million bucks for our rebuild (in a neighborhood where not a single house has ever sold for that much), and there are still weeks at a time when the house sits with nothing happening, because he's juggling too many projects with not enough qualified employees/subs to manage it all.
OTOH, buying and moving? We had to move into an apartment, and it is ridiculous how much unexpected $ we dropped on stupid things like cabinet organizers (because the old ones didn't fit the new kitchen) and new storage/furniture to fit into the different spaces this apartment has (like, say, a 12" deep console table for car keys, because that's all we can fit and still squeeze by). And this was for a fully-furnished apartment. Change that to a new home, and now you're adding new paint, window treatments, probably new/redone flooring, a new faucet here, a new hot water heater there, and oh that tile is ugly, and now our couch doesn't fit, etc. And you're then coordinating and managing all of that with two small kids and a full-time job.
The other thing is that right now, you don't actually know what your long-term financial situation is. You think your DW will continue to not WOH, and that may be the case, but maybe having 2 kids under 3 will send her screaming for a nanny.* Or maybe your baby will have big medical bills or special needs and your budget will be even tighter than you anticipate. You can't actually know any of this stuff for probably the next year at least.
The good news is that you don't actually have to make this decision right away. The baby can sleep in your room for a while, and can then bunk with the toddler. It may not be ideal, but it is completely feasible for some period of time while you're figuring out what you actually need and what your long-term priorities are.
I know I sound like Debbie Downer, and I'm not trying to be all doom and gloom. But it seems to me like the downside of making the wrong choice here is long-term financial stress, which can seriously affect your ability to live the lives you want and enjoy yourselves along the way. Whereas the downside of not deciding just yet is maybe a few months of the baby sharing the toddler's room. Comparing the downsides, the choice seems rather obvious, no?
Congratulations and good luck!
*No disparagement meant here. My two-under-five left me ridiculously grateful for daycare. ;-)