How can I get all my messages back on my new iPhone?

Using the same Apple ID and restoring a backup of the previous device to the new or using the same Apple ID transferring the contents from old to new, or using the same Apple ID and with iCloud Messages enabled, are the usual paths.

When moving to a new iPhone, the backup save and restore, or the contents transfer, are typical.

If setting up the iPhone as new, then Messages stored locally on the old iPhone will not be available, though Messages configured with iCloud Messages support will be.

If the Messages were deleted, then: How to Recover Deleted Messages in the Ap… - Apple Community