The main issue is which version of electron is supported on your platform. According to this after electron v27 macOs 10.13/10.14 are no longer supported.
Furthermore according to this obsidian v1.5.8 upgraded to electron v28, and this then enforces the previously mentioned platform support, so you can’t run that installer version on macOs 10.13/10.14.
In other words, you need to install the v1.5.3 version of Obsidian to make electron happy, and allow the install. When that is installed you can auto-update Obsidian as long as the installer version doesn’t need a change.
And there might be changes in newer installer version that might cause strange behaviour of newer versions of Obsidian.
But as long as you keep the installer version on 1.5.3, you should be able to keep running Obsidian (even with newer versions of Obsidian).