Will a notification on the desktop transfer from one iMac to another

I am transferring the contents from one iMac to a newer iMac. The older is running Ventura and the newer Sequoia. For some time, I have been getting a notification on my desktop which reads as follows...

'Required managed update.

An update is scheduled to automatically installed tonight. This update requires at least 50% battery or connection to a power source. Your computer will restart to perform the update. No deferrals remaining.' 

I've consulted Apple support and apple communities and have as yet to find a way to delete it. So, my question is: will this notification transfer to my new iMac? If I should choose to do the transfer manually, can I be assured that the update won't transfer?

There is another notification which seems to happen with the Safari browser. It appears when I open Safari, and basically says that on 3 separate websites I have used, there is a data breach, and to click on the link to have it repaired. I have never clicked on the link, but also have never had a problem with the notification and the performance of my computer. Again, my question would be, does this notification transfer into my new computer?

Any advice on this would be great!

Andrew