Old files from a backup are corrupting my new 2025 Macbook Pro.

First Macbook was used brand new from 2009 to 2018. When it died I did a Time Machine backup onto an external drive. Flash forward to 2025 I buy a brand new MBPro, move every thing over, and its having issues with photos and imessage not completing icloud sync and I’m unable to send or receive photo messages from my imessage on Mac, they show up on phones as blank bubbles. They had me make a test account and this didn’t happen which confirms it’s an issue with my backup. I’ve been calling apple support all week. The last person went through my system library and pulled out files that have “@me” (MobileMe) or “DotMac” in them. He told me these files are from the storag systems Apple used before iCloud and these were potentially in conflict my iCloud syncing correctly. This fixed my Sync issue, but I still can’t send or receive imessage photos on my MB. At the moment they are having me reinstall Sequoia. If it doesn’t work I’m going to have to wipe the whole thing and do an icloud sync. I’m just wondering where I went wrong here and want to understand this situation fully if I have to do a wipe. What’s the difference between a Time Machine backup on an external drive vs cloud? Wouldn’t broken files still be there after a reboot/cloud sync anyway? Is that not would I did the first time? If not what will I lose exactly? I know TM is supposed to cover pictures/videos/docs but given the situation I’m worried some of those things could be in incorrect “old” places or tied to my “@me” id and I’ll lose them. I read that MobileMe/DotMac was a system that stored pics/videos/documents. If that doesn’t work then what the hell what do I even do?