From @westonruter in #4980 (comment).

We should export to JS this logic from PHP:

$has_amp_support = current_theme_supports( 'amp' ) || in_array( get_stylesheet(), AMP_Core_Theme_Sanitizer::get_supported_themes(), true );

Note I'm intentionally using get_stylesheet() here as opposed to get_template() because child themes of core themes are often not AMP-compatible.

Nevertheless, we may want to hold off on doing this until I finish my work on the Reader theme loading because this changes how the amp theme support is mutated (or not).

There's also a case to do something similar for Reader mode, for themes that don't have amp theme support and yet have an amp directory, which is captured by this logic at the moment:

We may want to mention that the active theme has special legacy Reader mode support, and also indicate that in the list of Reader themes.