It's an intriguing situation. It sounds like your MBP is not properly handling Messages in iCloud, since the unintentionally deleted conversation should have also been deleted from your iPhone. You could go through this checklist to make sure all the settings are showing up as they should:
iPhone and Mac both logged in to same Apple ID. Try logging off and logging on if necessary.
iPhone Settings => Messages shows iMessage as "on" (sometimes toggling this off and then on fixes some things)
iPhone Settings => Messages shows Send & Receive showing both phone number and email (Apple ID)
iPhone Settings => Messages shows Text Message Forwarding and your Mac is listed and shown as "on" there.
iPhone Settings => Messages shows Send as SMS "on" and MMS Messaging and Group Messaging both "on"
On the Mac: Messages => Preferences => iMessage tab shows same and correct Apple ID and "You can be reached for messages at" indicates both phone number and Apple ID (email), and "start new conversations from" indicates the phone number.
* Don't see the Text Message Forwarding setting on your iPhone? Go to Settings > Messages, turn off iMessage, turn it back on, tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.
Assuming this is all correct (check each item in the above list, any of them being not right could cause irregularities), since it is just 120 messages, you can simply forward each one to your phone number, which will cause them to reappear on your Mac. This will take a few seconds per message, in about 10 minutes you'll be done. Less time than you have spent trying to figure it out!
Then, once the desired messages are safely back on the Mac, you can try other things to try to get the MBP "behaving" again. Such as disabling its Messages in iCloud, logging it entirely out of the Apple ID, logging it back in, and then re-enabling iCloud messaging on the MBP. Or you could leave it alone, but it might continue to not sync fully. Have you done a little "audit" to see what else might be different between the MBP and the iPhone in terms of messages? Are there any other discrepancies? What is different about that conversation that is anomalous -- is it SMS as opposed to iMessage or vice versa, for instance? That could be a clue.