If I make changes, updates or modifications to MPL-2.0 licensed code and start offering it as a service (SaaS) am I required to disclose those changes? Or does MPL-2.0 only require disclosing changes if the code was distributed as files?
The MPL-2.0 license does not define the term "distribution", so the normal interpretation applies. This means that distribution only takes place when files are transferred from one party to another.
For server-side software offered in a SaaS setting, no transfer of the software takes place and thus also no distribution.
When you distribute MPL-licensed software, you are not required to explicitly mention changes, but you are required to make the source code available alongside any binary distribution.