Contact Form: deprecate module code

[monsieur-z]

The Contact Form module code has been brought over to the Jetpack Forms package. It is time to deprecate the module codebase (the module itself will technically still exist).

Project thread: pf5801-Aj-p2

## Step 1
- [ ] https://github.com/Automattic/jetpack/issues/35654
- [ ] https://github.com/Automattic/jetpack/issues/35653
- [ ] https://github.com/Automattic/jetpack/issues/35655
- [ ] https://github.com/Automattic/jetpack/issues/35656
- [ ] https://github.com/Automattic/jetpack/issues/35657

## Step 2
- [ ] https://github.com/Automattic/jetpack/issues/35658
- [ ] https://github.com/Automattic/jetpack/issues/35659
- [ ] https://github.com/Automattic/jetpack/issues/35660
- [ ] https://github.com/Automattic/jetpack/issues/35661
- [ ] https://github.com/Automattic/jetpack/issues/35662
- [ ] https://github.com/Automattic/jetpack/issues/35663
- [ ] https://github.com/Automattic/jetpack/issues/35664