Jetpack modules don't get activated on the first try

### Impacted plugin

Jetpack

### Steps to Reproduce

1. Create dummy plugins in `wp-content/plugins/grunion-contact-form/grunion-contact-form.php` and `wp-content/plugins/mullet/mullet-contact-form.php`. Activate both.
2. Go into Jetpack's module settings and deactivate the Contact Form module if needed.
3. Activate the Contact Form module.
4. The plugin will get deactivated, but the module will stay inactive.
5. Try to activate the module again, it will get activated.

### A clear and concise description of what you expected to happen.

The module should get activated on the first try.

### What actually happened

Due to the plugins that needed to be disabled, the module didn't get activated on the first try.

### Browser

_No response_

### Other information

More info: p1672959530701559-slack-CBG1CP4EN

### Platform (Simple, Atomic, or both?)

Self-hosted

### Reproducibility

Consistent

### Severity

Some (< 50%)

### Available workarounds?

There is no user impact

### Workaround details

_No response_

Reproduce the issue using the dummy plugins at wp-content/plugins/grunion-contact-form/grunion-contact-form.php and wp-content/plugins/mullet/mullet-contact-form.php, then activate and deactivate the Contact Form module in Jetpack's module settings. Trace the activation sequence and verify that the module is active after the first attempt while required plugins are disabled.

Written by the indexing model from the issue text.