How do I fix delayed iMessage syncing between two Macs?

Hi. I have two Macs. One for home (my main one), and one for school. My main one is running sonoma which is a 2019 MBA, and my school one is a 2011 MBA running high sierra (both latest compatible software for them). I have this issue where sometimes messages that I receive or I send only appear on one mac. For example, I send the message to somebody on my home mac, and I receive the message of the person responding to me on my school one, but the message only appears on my school one. The message can take up to two days to appear on both of my macs. Both of them online/awake at the same time and it will not appear. Even restarting the mac or quitting iMessages and reopening it does not work. I am pretty confident this is not a thing of high sierra being too old because I had the issue with other macs with later software. Though, on my iPhone, I don’t have any issues with iMessage. I don’t use my iPhone much, and most of the time I keep it in shutdown mode, maybe this could explain why iMessage is getting issues because it can’t talk to my macs? Thank you in advance, have a good day.

[Re-Titled by Moderator]

Original Title: iMessages not syncing