Your company seem to have a significant technical debt in environments, tooling, test automation, CI/CD, that is slowing down releases. Is that a problem acknowledged in your org? Will you get support for continuing changes and is there an understanding of what is a good enough level?
Would a fixed weekly or bi-weekly schedule work? Both devs and QA can plan their work accordingly. For example: devs and QA agree on what to work on next on a Thursday and how to test (acceptance criterias). Dev start development, QA prepare tests (functional and regression). Dev work for a week, tests and feature freezes code next Thursday. QA starts acceptance test on Friday, they ping-pong Fri-Mon-Tue, regression test and full code freeze on Wednesday, release on Thursday. If quality of the code and tooling makes the process smooth enough, then a similar weekly cycle could also be possible.
Gradually increasing test automation could speed up the whole process. Devs and QA can write and maintain automated tests together.
Feature flags could help isolating bugs that are discovered late in the process.
If there are several rounds between devs and QA, then a root cause analysis can help there as well. Are devs and QA aligned on how to test? Are devs testing enough? Is QA giving enough info for devs on the bugs found? Etc.
Your friend could walk you through their business processes and how they plan to use the third-party software. It would be a good chance to document all that knowledge.
You could also take a look on the documentation of Odoo.