You can bring all of that history and you MMS files over.
Install SMS Import / Export from Github.
https://github.com/tmo1/sms-ie
A preferred way to install apps from Github is to use Obtanium to do your installs
https://github.com/ImranR98/Obtainium
A lot of people have justifiable concerns about using the FDroid app store, but it does have an easier learning curve than Obtanium when you're just starting out and everything you're trying to do is new and unfamiliar. Instructions to install the FDroid app store are on their home page.
https://f-droid.org/en/
Then use the FDroid app store as you would the Google app store to install the SMS Import / Export app:
https://f-droid.org/packages/com.github.tmo1.sms_ie/
Whether you use Obtanium or FDroid, the SMS Import / Export app will create a backup file of all your SMS messages, MMS images, your call log, and block lists. Then use the same program on your new phone installation to import that data from the backup file you created.