I personally use Mempalace which is perfect to shrink down the size of the memory to be used by Claude Code. It is open source; fully integrated in Claude (plugin instead of MCP); fully working in local (python application and database); fast to be queried and to be installed. My suggestion is to instruct Claude to use it as PRIMARY MEMORY and to save in there everytime you decide that it's time to save or in the end of the session.
Also I suggest to save the Mempalace memory database in a separated github repository, so to have it always available for all the devs in the project.