Stash won't parse EE embeds at all (this is by design) so you'll need to use a Stash embed instead. When you use process="end" the tag is replaced with a marker and 'post-processed' after the EE parser has completed parsing, and then replaced into the final template output. Therefore, it is up to the post-processed tag to do any parsing that might be required of the tags that it encloses.
With that in mind, you have two options here for the stash embed: make the stash embed behave like a standard EE tag and ask get_list to parse it as a tag, or include the stash embed at the start of template processing before the EE parser replaces the wrapping get_list tag with a marker:
{exp:stash:get_list name="sidebar" process="end" parse_tags="yes"}
{stash:embed name="sidebar-events" stash:limit="3" process="inline"}
{/exp:stash:get_list}
{exp:stash:get_list name="sidebar" process="end" parse_tags="yes"}
{stash:embed name="sidebar-events" stash:limit="3" process="start"}
{/exp:stash:get_list}