Flag to allow a group to be visible for "share to group" when you're not a member
Description
Currently, you can't share to a group you're not a member of. This means if you create (as an arbitrary user) a new repo - you can't go and share it to "companywide-code-reviewers" or similar. So instead, you have to grant to a user that is a member, and then have that user go and (as new owner) share the project to the group, and then remove the individual share. That's ugly in the case of sharing with elevated permissions, and worse in the case where you want to share only limited rights to the target group.
Proposal
Add a flag to the groups like you have now for being able to request access/etc - "Allow group to be visible to all for 'Share to group'" If that flag is set, it will be selectable and in autocomplete for any user.
Might consider: Group Visibility for Sharing: [Members | Internal] with the default being 'Members'
Another option - if the group itself is marked as public or internal - simply make it available for selection regardless of membership.