You can set your End Frame visually by selecting the last non-black Frame of your footage in the VSE and then hovering your mouse over the Timeline and pressing E for End Frame (as indicated in the Frame menu) or S for Start Frame to set it as your current frame (that's the green vertical line in the VSEs Sequencer View and in the Timeline).
But make sure, as in your case you did this "wrong", that you unselect the "Use an alternative start/end frame range for animation playback and OpenGL renders instead of the Render properties start/end frame range".
As you can see in your Screenshot, you checked it:
This causes your unwanted behaviour.
If it's checked, your Timeline Frame Range Settings only effect Playback (Ctrl+A), but when you render your Movie (Ctrl+F12), the Render Properties Frame Range will be used (both differ in your case 9357/250).
The 250 Frames are just 10.4 seconds (or 10 Seconds plus 10 Frames, you already stepped one frame backwards in your screenshot to 10+09) which were rendered in your case. The 9357 are nearly 6:30 mins, so this should be reduced to about 24 frames/sec * 60 sec/min * 3 min = 4320 Frames.
use_preview_range and then your End Frame in your Timeline should show 250 as well as it is now set to in your Render Properties. You then need to set your End Frame to approximately the mentioned 4320 and you're fine.
Oh and usually you should set your Start Frame to 1, not 0. ;-) This makes your End Frame show/match your actual Numbers of Frames, else you need to increase it by one to get your final Frame Amount.