Can You Play Color Block Jam on Multiple Devices?

Does a second device sync automatically?

No automatic sync is currently available through Google or Apple login, according to the official article. The safest assumption is that a new installation starts without the progress on your old device.

What should you keep?

Keep the old device, note the level shown in the game, and contact support from the in-game Account path. If you are also using a walkthrough, keep its URL and opening-board notes separate so you can identify a level mismatch later.

What should you avoid?

Do not uninstall the old copy first. The saving progress article explains the same limitation and why support should come before a reinstall.