issue in HDMI TO VGA conversion

For any future googler who comes to this question, here is my solution. I got it to work by setting the refresh rate of the external monitor to be the same as my laptop monitor, 60Hz in my situation. My system is Windows 10.

The settings can be found at Settings -> Display -> Advanced display settings -> Display adapter properties for Display 2 (for external monitor) -> Adapter -> List All Modes -> select a mode such that it uses the same (or higher) Refresh rate as the laptop monitor.

What you descibe sounds most like the adapter is doing the best it can for what it is.
There are "sync" settings in (only) some VGA monitors that could compensate completly for a sloppy conversion.
The digital to analog converters and VGA monitors can also generally run best at specific resolutions, or aspect ratios. As you discovered they can still "work" at many resolutions, just a bit off.

HDMI output itself is very malable via many of the display drivers own software. It is possible you could tweak resolution (and the aspect of it) The display software, and or the monitor to get an acceptable picture. It is common for HDMI output to have to be adjusted in display properties for the GPU software to compensate for Overscan.

Are they only capable of a few resolutions NO. Is 1366x768 a weird resolution that a cheap converter might leave some blank space or offset picture? YES. Is it possible that even the best converter would have some offset or issue? YES. If it was going to an old-school CRT high-end monitor could most of it be compensated for? Probably.

Find everything to adjust, and adjust everything, hours later you might get it closer.

Could be the automatic overscan compensation. Unfortunately I don't have a Windows notebook anymore, so I can't tell you where exactly to find the setting. It's in the Intel Graphics Control Panel.

Of course, this all applies only if you're actually able to set the correct resolution in Windows.