ci: Move the READMEs test into another test phase to reduce VM load

The split of integration tests made it possible to run these concurrently. Unfortunately the load to the VM machine was too great.

Split the integration tests into several smaller stages so that they don't run at the same time.

Fixes: #106 (closed) Fixes: #110 (closed) Fixes: #111 (closed) Fixes: #115 (closed) Fixes: #116 (closed) Fixes: #117 (closed)