The control center on my Apple SE watch does not come up when I drag from the bottom of the watch face.

See if this helps:

For WatchOS 8:

How to Use Control Center on Apple Watch – Apple Support

Eg: says:

From the watch face, swipe up.

From other screens, touch and hold the bottom of the screen, then swipe up.

Hope this helps :-)

PS: You may need to restart your watch first, to get it working right

How to: Restart Apple Watch – Apple Support

Thank you for letting us know you were able to solve the problem.

Cheers :-)