No, but most connectivity metrics include some frequency or time-frequency analysis.
https://neuroimage.usc.edu/brainstorm/Tutorials/Connectivity2
However, I am stuck in the second step because I cannot run any source analysis on time-freq datatype which is the output of the hilbert-transform.
In the line above, you say "Source localization > hilbert-transform (envelop) on the source timeseries". This is correct way of proceeding, and does not require "any source analysis on time-freq datatype" (which is not possible).
If you really want to limit the source estimation to a specific frequency band, then filter all your recordings (including the noise recordings), and then estimate the sources.
For discussing new topics, please create new threads on the forum - this will make it easier to search the forum in the future. Btw, this topic of "source reconstruction of time-frequency decomposition" has been discussed a few times in the past, you can probably find these threads on the forum.