I haven't tested this new feature myself yet, but it looks like Airtable designed this feature to only work within a single team that is using Airtable and is logging into Airtable with their own Airtable accounts.
I would recommend accomplishing this in a completely different way by embedding webhook links in your Slack messages using Make's Slack integrations and Make's webhooks.
I describe how to do this with email messages in this episode of the BuiltOnAir podcast, but my instructions can be easily modified to do it with Slack instead of email.
p.s. If you’d like to hire an expert Airtable consultant to help you with any of this, please feel free to contact me through my website: Airtable consulting — ScottWorld
https://youtu.be/58urboTLZck?si=hdnYGhpAIhzRilh6