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At the end of the first email you're asked to reply if you're not interested "and I won't bother you further". The second email is just another push to try and get you to take the bait, and the third is more of the same.
The whole thing reminds me of some spammer who proudly and publicly told everyone about their tactics on their blog a while back [0], so I really hope most companies know better than to try this BS. Anyone else with a similar experience?
[0] : https://www.wisp.blog/blog/how-i-use-ai-agents-to-send-1000-personalized-email-for-outreach