Hmm. Almost!
The functionality discussed there is one that I assumed was already in 7.9, because there is already the option: Automatically update agent binaries to use the latest minor version. (Same issue as this person: Manual manage agent binary version)
Now that this feature comes in, I'll see whether the upgrading also works for Bugfix releases, meaning e.g. 7.10.0 -> 7.10.1
Do you happen to know if I only need my Stack at 7.10 for upgrading to work, or also the agent binary on 7.10?