Another really good way to do better at research is build the "Bob" Wonder, it requires that you research Strong AI Tech, and adds 300% to the base research at ALL of your Core worlds, plus nice adjacency bonuses to neighboring tiles. See the following Discord message, it also gives the list of Techs that you need to research to get to Strong AI Tech.
Build the Bob Wonder next to several other Buildings with high levels of Research and get a lot of research.
see this for a screenshot of my HW, in 2313
I have both the Bob Wonder and the Ascension Gate, plus a lot of other Research Wonders and Buildings built on my HW. Look at all of the bonuses to research that I am getting on my HW.
I am playing as the Corporate Sector, and I share my Home Sector with 4 other Races, i.e. so I am not getting all of the research points produced in my Home Sector. I did conquer one of the Races sharing my Home Sector.
When I rushed built the Ascension Gate to get this Screenshot, I also got a Tech Victory for my game (combined with everything else that I have done and researched in that game).
I am only continuing to play this game because I am waiting on 0.65 to start a new game.