Thank you for the follow-up. Based on the info provided, I believe the issue is tied into how the new subscriber trigger functions.
New Subscriber automations, sometimes referred to as welcome emails, are only set to trigger off of brand new contacts signing up directly through sign-up forms. If you set the automation to be new list additions, that will trigger off any contacts being added to the speicified list(s), whether you manually add them or they sign up through a connected form, whether they're existing contacts or entirely new subscribers.
Make sure to check out this overview of automation triggers and how they function for more info.
Regarding the the landing pages, they are not embeddable, since they're meant to be linkable or pasted as raw URLs essentially anywhere.
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