Kylie, I’m not sure if you ended up finding a remedy for problem yet, I found your post after experiencing the same issue...
MMS enabled, both in settings and via carrier. In Australia, our latest carrier format for mobile (cellular) data is 5G, which apparently optimises iPhone 12 and other new brands of smart phone using mobile data. But... possibly similarly in US, MMS and other forms of encrypted data can be blocked, both on wifi and mobile data.
This can be adjusted by changing SIM, either physical SIM or eSIM. Then I guarantee you will be able to send pictures, videos, group pictures, etc. Essentially you need to “dumb down” your iPhone 12’s abilities, using the predecessor of your current SIM. Your last phone did not have capabilities of this one, so it would not have blocked anything. This will not adversely affect your phone. Frankly, many of the so-called awesome features are a pain in the butt, Face ID sucks, I now only use PIN, and this new security feature is a massive irritation. So downgrade the SIM.
my last phone was iPhone X. No problems ever.... if it ain’t broke, why fix it?