is Webview safe to use?

I hadn't used Webview before because my previous projects used the NJWS extension.

But now that NWJS is being retired, I have to look at it since it sounds like webview is the new primary export option.

I noticed that you can't bundle the browser with the game, is that going to be safe long term in the years to come?

Will my game still work the same way consistently, even if they change the way the browser/Edge works in later years? And what if future Windows versions change the way they do the browser? Will my game be safe?

I've also heard that it's not good because it doesn't work with Steam overlay or something? If so that makes it unusable for me, because Steam is the primary audience.

There's a github issue talking about this exporter being broken with Steam:

github.com/Scirra/Construct-bugs/issues/8328

I noticed that you can't bundle the browser with the game

You can actually, with the "fixed" distribution mode. It's documented here.

Will my game still work the same way consistently, even if they change the way the browser/Edge works in later years? And what if future Windows versions change the way they do the browser? Will my game be safe?

Even with the default "evergreen" (auto-updating) mode I wouldn't expect there to be any problems. Web exports from over a decade ago generally still work fine, and it's basically the same situation with WebView2 exports. Our Android export option has always used auto-updating web views, it's one of the most-used export options in Construct, and I can't recall the browser engine auto-updating ever causing a problem. So I think while the browser engine updating and breaking the game is a theoretical concern, in practice I don't think it is. Of course if anything did break backwards-compatibility, we'd release a patch immediately. There's also other system updates that could break your game, like a broken graphics driver roll-out. Part of supporting software just means keeping an eye on it.

I've also heard that it's not good because it doesn't work with Steam overlay or something?

The Steam in-game overlay isn't supported - we've gone to great lengths to try to get it working, but the way Valve have implemented it means there's just no way to even work around it no matter what we do. However Steam falls back to showing the actual Steam UI when the in-game overlay is not supported, so it's not something we consider a blocker for moving to WebView2; if you care about having the in-game overlay you'll need to contact Valve as unfortunately it seems to be one of the things that is outside our control. The rest of the Steam features work fine and the Steamworks plugin for WebView2 actually has more other features now.