On your MacBook Air, open Messages >> Filter >> Manage Filtering and check Screen unknown senders.
If it is enabled, turn it off. Apple says messages from unknown senders are otherwise filtered into a separate folder and you may not receive notifications for them.
Screen and filter text messages on Mac
You should also check Messages >> Filter >> Unknown Senders.
Messages from numbers that are not in your Contacts can appear there; you can select an important sender and choose Mark as Known.
Screen and filter messages from unknown senders
Also check Messages >> Filter >> Spam.
Apple says messages identified as spam are moved there and removed from the normal conversation list.
If a legitimate message is there, select it and choose Not Spam. You can also turn off Filter spam under Manage Filtering.
Report spam and block senders on Mac
Apple specifically identifies screening unknown senders as a new Messages feature in macOS Tahoe, so this is the first setting I would check on your new Mac.
Apple's relevant instructions are here
Screen and filter text messages on Mac
Report spam and block senders on Mac
What's new in Messages on Mac — macOS Tahoe