Getting an array of ids from an array of eager-loaded elements within Twig
You would just loop the entry models to collect the IDs (looks ugly, but it's a simple and efficient for loop). But in case you do not need anything else from the models, I'd actually expect your previous approach using the ids method to have better performance.

{% set ids = [] %}
{% for entry in entry.myEagerLoadedEntries %}
    {% set ids = ids|merge([entry.id]) %}
{% endfor %}