The limitation isn't there, it's deliberate. If you look when you connect to a monitor, the resolutions you can select for a game are resolutions detected by the Deck to be supported by the monitor. The Deck deliberately doesn't go for the highest supported resolution by Default, I imagine this is because the Deck's hardware is optimized for lower-resolution play, which is why it usually just stops at 1280x720p cuz the deck itself is 1280x800p which is pretty close.

Some games will also save the resolution when it generates the default graphical settings and then save that and reuse that. So if you then plug in an external display, the game doesn't even look for that. It loads the last settings which would be 720p.

Also the Deck runs games under gamescope which has its own upscaling. So it probably sets the virtual screen to be the deck's native resolution regardless of what's plugged in, and hope FSR is good enough and minimize the need to also have to switch other graphical settings for the game to run properly at higher resolution.

Not sure why it would do that for streamed games though. How's the game on the PC even aware of the resolution of the Deck?

Consoles don't do that, they have a set resolution and try to use that even if the monitor supports higher res, the reason is that a console has a limited hardware and knows its limitations, that way they can ensure the best user experience. The Steam Deck works primarily as a console, but without the usual closed off limitations so you can change the resolution if you know that the specific game you're trying to play will support it, but as a general the deck plays it safe and uses the same resolution it would use for the integrated screen.

Also you need to think on the cluster fuck it would be if you're playing the game in 4k then unplug your deck and now you have a 4k game downscaled to fit a 1280x800 screen.

Yes this is annoying. I like to play games docked, and in order to get them working correctly I have to manually tell Steam to use 1080p resolution for every game. This then gives you more options within the game settings (rather than maxing out at 1200x800) whilst docked. But in most cases I have to then change the in-game setting each time I go from docked to portable.

It does feel like docking is an afterthought with the Steam Deck. I was expecting something more akin to the Switch which has a flawless docking experience. I hope SteamOS improves on this in future.

you mean changing the resolution of the games when you switch from playing in handheld mode to on an external screen? that would have to be done by each game, most games save their graphics settings and only re-autodetect resolutions when they fail to set the one in the config

there is not a standard protocol for this, I recommend just using full screen windowed when available as that tends to act as a maximization to the screen

Do you mean in games or in the steam os itself? If steam os has the right resolution you can set the per game resolution option to native.