I'd love if there was a way for your addon to remember the tab/category/page and scroll position I was last on in one of the tabs that are added by your addon, so that I don't have to navigate back to it every time I reopen the achievement interface.

For reference, I know about the "Reset view on open" setting found in your Key Bindings settings page, but disabling this only affects the default Achievements tab and nothing else.

You can keybind other tabs. This should meet your needs. See options -> General -> Keybindings

Not entirely. When using the search bar and clicking on an achievement via that, it still resets the position back to the summary page when reopening the interface.

One thing I tried to do to work around all of this, was to disable all of the extra tabs, but it still navigates into the hidden tabs when using the search feature, so that workaround wasn't effective.

This was implemented in 90f3b45 and released with version 50.0