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That bar is part of GNOME Shell, and user applications don't get to mess around with the shell. You need to look into writing [shell extensions](https://gjs.guide/extensions/) to modify that in a general way.

One common thing for an application to want is to show a status icon, in which case you could use an extension like [this one](https://extensions.gnome.org/extension/615/appindicator-support/) and use any of the supported AppIndicator-like standards in your user application. Unfortunately, if you're developing an application for others to use, there's no way for you to force such icons to appear in the shell without your users installing an extension like the linked one. If you require native support without an extension, you'll have to settle for a GNotification, which won't appear in the bar.