I need my Imessages from a broken15 pro max

I can access the 15 pro max. But it will turn on. So if I sign on to icloud and toggle on backups from icloud.com on my windows laptop. Will my imessages then appear on my icloud. Reason it was turned off because of the storage was full . If storage is a issue, can I buy some icloud storage on the icloud + and then retrieve my data

Ps

I do have a older iPad if there's anything I could do with that in order to help with the process.