chore(web): move common/core/web to common/web

Relates to #5816.

Moves folders under common/core/web to common/web:

* input-processor -> common/web/input-processor
* keyboard-processor -> common/web/keyboard-processor
* tools/recorder -> common/web/recorder
* tools/sentry-manager -> common/web/sentry-manager
* utils -> common/web/utils

Updates scripts and configuration to point to new folders.