Geo Replicables: Migrate mutations to Apollo

What does this MR do and why?

Closes Geo Replicables - Migrate GraphQL to Apollo fro... (#425584 - closed)

This change makes changes necessary to remove Vuex in favor of Apollo for the GraphQL served UI. This aligns with our documentation on not using Vuex with GraphQL.

This MR is part 2 of 2 as this feature is a bit larger of an effort. This MR is focused on the Mutation logic, the previous MR is focused on the fetching.

This change involves no customer facing changes.

Screenshots or screen recordings

All existing functionality persists

Screen_Recording_2025-08-04_at_12.38.56_PM

How to set up and validate locally

Setup Geo (optional)

Important: To properly test Geo you will need a separate GDK setup. Setup is straightforward but takes some time. Another option is to validate the code functionally and if needed schedule a call to sync and I can screen share my instance.

1. Ensure no other GDKs are running. gdk stop/gdk kill
2. Open an empty directory and install and run Geo with the one-line command found on the Easy installation instructions
3. Access your primary and secondary Geo instances via 127.0.0.1:3000 and 127.0.0.1:3001.

Testing

1. Access your primary GDK Geo Page (127.0.0.1:3000/admin/geo)
2. Scroll down to the very bottom Replication details section
3. Click one of the blue links (ex: Project Repositories)
4. Ensure all expected UI functionality persists

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #425584 (closed)