Hey, thanks for asking! Here goes kind of a long reply.

JWST won't be able to contribute here. The planets are non transiting.

The first instrument which should be able to characterise them is ANDES, a spectrograph for the ELT (in design phase). ANDES is expected to have a mode optimized to study atmospheres of exoplanets in reflected light. After that, the ESA LIFE mission (in concept phase), which will use nulling interpherometry to "hide" the stellar light and study the thermal emission of planets. In any case, it won't be before 2031 (ANDES) or ~2050 (LIFE). I do not know if NASA has anything in the pipeline for this science case.

We picked GJ 1002 because is one of the closest stars to the Sun. It is also a M-dwarfs (similar to Proxima), and a very low activity star. This fulfils quite a few goals in one go. First of all, we want a census of the solar vicinity. There are not that many transiting systems nearby, so K2 and TESS had not contributed all that much here. Then being an Mdwarf means that the planetary signals are large for small planets (easy to detect), and the orbital periods are short (easy to sample several times). The spectra odñf Mdwarfs also has lots of absorption lines, which means we can measure good velocities even if the star is faint. Then low activity means once again easy to deal with. Lastly, nearby also means large projected separation between the planets and the star when looking from here, which is important for the characterization with the missions I wrote before.

I'm not sure we can talk about opening any flood gates. There seem to be lots of earth más planets out there, but the detection process has a lot of bottlenecks. Telescope time (this work needed roughly 100 hours of telescope time between CÁRMENES and ESPRESSO). Telescopes are typically shared between different communities, research topics and research teams. Getting 100 hours for a single target is not easy. Then data processing and analysis is also still not where it needs to be. We are mostly getting the easy cases. We have come a long way (it used to be easy Jupiters, now it is easy Earths), but there is still a long way to go. RVs are also more difficult to deal with than transit photometry. No one has figured a way of automatically analyse thousands of time series and reliable detect the planets. It still requires a system by system approach.

Just to show how slow this things are. I'm in the ESPRESSO science team. We started observing this star in 2019. I spotted one of the planets of the system in summer 2021. In winter I was told that the Cármenes team also had a lot of data (from 2016!). In January a presented my collegues a solid case for a 2 planet system, but with a need to collaborate. In spring both teams had evaluated the full dataset and agreed to collaborate. In early summer I finished the definitive analysis, and the first draft of the article. It was circulated in both teams and modified according to the suggestions and comments of roughly 40 people. We submitted to the journal in September. A month later we got the report from the referee, which triggered a complete reanalysis to test the robustness of the analysis we had originally presented. When it was confirmed to be robust, the article was accepted for publication (late November). It has been roughly 6 years of work (between both teams), with a year and a half of intense work. The whole analysis process was very handcrafted, requiring understanding the star quite well. As long as we need to continue working like this, it will be very difficult to get lots of planets quickly.

We are getting better, but it is still very slow.