I think this extension is quite simple and generally safe to use for two reasons:
Firstly, on Q. When does HTTPS Everywhere protect me? When does it not protect me? section on HTTPS Everywhere website FAQ page
HTTPS Everywhere depends entirely on the security features of the
individual web sites that you use; it activates those security
features, but it can't create them if they don't already exist.
This means the extension simply turn on HTTPS automatically if possible and does not communicate between the user's browser and the website.
Secondly, it is open sourced and the source code is public. It means anyone can access and read how the extension works if possible.
However, in my opinion, the description of the extension seems misleading, because it claims to 'encrypts your communications' on their website. This extension simply switches from http to https if possible and doesn't do anything with the transmission of the data.