Hi! I'm the fabled "project manager" that we'd like to hire! Helping run Bevy has been an incredible experience, and I'm very excited about the idea of being able to do this full-time. There are a ton of efforts I'd like to lead, and even more that I'd like to be able to help nudge along.
My personal opinion (and I don't speak for anyone else) is that Bevy 0.13 is usable for 2D games if you use Tiled as your editor. Most 3D games will have to wait until 0.14 (the next release) though, since there isn't animation blending yet (though note [1]), and most 3D games need that. Since I landed animation blending in 0.14, once that version is out I think Bevy will be ready for advanced users who aren't afraid to get their hands dirty to build serious stuff, using space_editor as your editor.
Physics is 3rd party currently, but it's on our roadmap for "some day, definitely". Writing your own physics engine is... a lot of work, and not something that I'm excited to volunteer the engine itself for immediately.
There are two popular physics engines used in Bevy today: Rapier[0] and bevy_xpbd[1]. Both are candidates for upstreaming, but both have their own challenges. I've spent some time working with each of the authors recently, laying out my concerns and thoughts.
On the Rapier side, the documentation is sparse and aggressively mathematical, it uses a distinct math library from the rest of Bevy, the API to work with Bevy is sometimes clunky and unidiomatic, and it can be quite hard to figure out how to do Ordinary Game Dev Things with it.
On the bevy_xpbd side, the performance is subpar, there can be physical stability issues, it's generally immature, and the XPBD solver that they use is, unbeknownst to the young author at the time of the crate's creation, patented by NVIDIA [2] :(
Both of them are working to improve (and I'm very pleased to see that even independent of this discussion), but neither is ready for imminent official endorsement or integration. One day we'll have a Blessed Choice though.
As for telling people "go forth and build your game!": things are stabilizing, and key functionality gaps are gradually getting filled. I have a terrible tendency to be overly honest, even in my marketing text, so there's going to be a long period of time where the actual answer is "it depends on what you're making".
Today, if you're building a weird game-adjacent bit of software (think CAD) for desktop platforms: totally ready! There are several very happy companies doing that. If you wanna mess around with Rust and nurse the Next Great Solo Dev Science-Based MMORPG Voxel Game: you'll have a blast, and it won't affect your chance of shipping a whit. If you want to build a simulation-y desktop game with lots of procedural generation and complex logic: honestly probably a good fit. You'll hit bugs and limitations, but you will in every other engine you use so...
If you want to ship high-performance web games, AAA graphics or mobile: eh, probably doable but dicey. If you want to ship to console: uh we'll find out if we can jump through all of the hoops and convince the right people to get Rust on console before the Steam Deck knockoffs devour the market (please!).
These will all slowly change, but an answer for "is it ready" will be hard to pin me down on until it's a full-fledged competitor to Unity, Unreal and Godot.