Finally, most of the beamformer code is working and issues are mostly resolved, which means that my focus has shifted to the user interface. I've made good progress on its development but don't yet have a working example although it's quite close. PRs that support this work have been or will soon be merged, including plotting complex-valued time-frequency objects, the widget abstraction (https://github.com/mne-tools/mne-python/pull/10913), adding provenance to time-frequency baseline corrections (https://github.com/mne-tools/mne-python/pull/10979), adding vector dynamic imaging of coherent sources (DICS) beamforming (https://github.com/mne-tools/mne-python/pull/10980) and computing cross-spectral density from time-frequency epochs (https://github.com/mne-tools/mne-python/pull/10986). Looking forward to having a snazzy new GUI soon!
On a side note with broader-level project organization in mind, I added a PR to sphinx-gallery to make the coverage of API entries in examples (https://github.com/sphinx-gallery/sphinx-gallery/pull/983).